What I am trying to do is to compare several versions of J.R.R. Tolkien's version of the Atlantis legend. J.R.R. Tolkien called his Atlantis island, Numenor, although it had several other names as well in the various versions he did.

The versions I have are mostly unfinished and published in the History of Middle-Earth with one exception, The Alkallabeth in The Silmarillion. The others are The Lost Road, which is in Volume five of the History of Middle-Earth, called The Lost Road, The Drowning of Anadune, The Notion Club Papers (especially part two), in Volume nine of the History of Middle-Earth, called Sauron Defeated and the Fall of Numenor, also in The Lost Road .
The different books I am using are, The Silmarillion, The Return of the King, Sauron Defeated and The Lost Road. There was at least one other unfinished Numenor tale, called Numenor, though I have no access to it. It was apparently written in the 1920's or the 1930's.
With the number of unfinished Numenor tales in existence, I would say it is safe to say that Tolkien was quite interested in the Atlantis legends.

The Notion Club Papers Version of The Downfall of Numenor:

One of Tolkien's unfinished tales was a new twist on both the Atlantis legend and his tale in the Silmarillion, called The Alkallabeth, which is his version of the legend of Atlantis. He called this tale The Notion Club Papers.

What is happening in the tale, is that at the beginning, two of the members (later a third joins them in the phenomenon, though not as strongly) of the Notion Club are finding memories of a past intruding on their lives, especially in dreams. In Alwin Lowdham, the dreams are characterized by words in a strange language, while in Jeremy, the dreams were more in the type of silent images. Sometimes the words and images would intrude upon the two in waking hours, especially when eagle-like clouds would float up over the horizon, western horizon especially, or during storms.
One of the two men had been called Aelfwine Earendel by his father while his mother modernized the name to Alwin. When Alwin was nine his father's ship completely disappeared in a calm sea in the Atlantic. Absolutely nothing was left of her. On that last voyage, Alwin's father had only three crew members. The significance of this comes in several forms:

First the parallels between that voyage and another especially famous one, that of Earendil with the last Silmaril. On his voyage, Earendil had only three crew and he too never came back.
Second, Alwin's father's ship was called the Earendel. From hints and parallels like this, I get the feeling that Alwin's father, found the "Straight Road", that some voyagers were lucky enough to find, though mostly only elves were allowed to find the "Straight Road" and depart Middle-Earth forever.

After his father disappeared, Alwin began to get the first fragments of the first of the three languages he was receiving. This language, he later found to be Anglo-Saxon. The other two languages were earlier languages from which Anglo-Saxon was descended.

I feel that as in the The Lord of the Rings it was said by Gandalf that when the blood of Numenor runs almost pure, or pure in somebody, that by strong use of will he or she could bend his/her sight wherever he or she chooses, often including the future or the past. The last two were easier done with some aid such as the palantir of Gondor. Gandalf himself admits to the temptation to use the palantir of Orthanc while it was in his possession (The Two Towers). As such was said, It seems to me that by some chance, Jeremy and Lowdham (possibly Ramer too) had almost straight decent from the Dunedain (meaning Men of the West) that had survived the downfall of Numenor. Over a period of time as they were discussing things such as dream training, these minor irruptions of Numenor were starting to make an appearance. One example would be on page 231 of Sauron Defeated, where Alwin, standing at a window cries, "Behold the Eagles of the Lords of the West! They are coming over Numenor!" . When others went to the window, there was a row of eagle-like clouds coming in from the west.
The significance of this is shown in both the Alkallabeth and in the tale of Aldarion and Erendis, in the Unfinished Tales, where at first the Valar show their displeasure with the Numenoreans with such portents as eagle-like clouds, sickness (before the Numenoreans were essentially immune to disease, and died at their own will, laying themselves down for the endless sleep at the time of their own choice. This changed gradually as the Numenoreans became jealous of the Eldar (elves) and their immortality.) and many other things. The eagle-like clouds were an especial constant along with drought, storms at sea and that sort of thing after the last of the kings of Numenor brought Sauron to live in Numenor.
Another quote from Alwin would be, "Curse him! May the darkness take him! May the earth open-" I would say that from the description surrounding that quote, that Alwin was cursing Sauron after Sauron had built a domed temple to Morgoth on the holy mountain, the Meneltarma. The description is of a cloud resembling smoke atop a dome Oxford.
Other times a sentence might slip out, often referring to Zigur. The word Zigur was later found to be the Adunaic name for Sauron. What I think is that Ramer, Jeremy and Alwin were reliving in a very compressed timeframe (a few months) the years preceding the downfall of Numenor and the actual downfall of Numenor.

Tolkien also had links to the usual name of Atlantis for the island in both this story and in the story the Lost Road. As I should have mentioned before, the other languages that Alwin was receiving, were later (I am not sure of the actual sequence of writing, did the Notion Club Papers precede the Alkallabeth or was it the other way around?) used in the Silmarillion. Alwin called them Avallonian, which in the Silmarillion and the Lord of the Rings was Quenya, the language of the High Elves. In Avallonian the name for Numenor was Atalante, which according to Alwin meant "She that has fallen down".

Tolkien's setting for the Downfall of Numenor was a massive storm, with regiment after regiment of eagle-like clouds blowing over the city of London, reminiscent of the storm in which the Downfall actually happened.

The actual downfall (as portrayed in the Alkallabeth) had a single long line of the cloud eagles floating in from the West, while Eru ( also known as Iluvitar, the One) removes Valinor (the dwelling place of the Valar) from Middle-Earth, creating a giant chasm into which Numenor slid. At the same time, the Meneltarma, never a volcano before, erupted with smoke and fire. There are several differences between the Alkallabeth, The Lost Road, The Fall of Numenor and The Notion Club Papers, as all but the Alkallabeth are still in manuscript form.
The downfall as portrayed in The Notion Club Papers, part two, was set in London, at one of the Notion Club member's rooms, mostly at a window facing west. It also seems to be from the point of view of somebody on a ship off the eastern coast of Numenor. At the time of the Downfall, there were (in the Notion Club papers) only nine ships off the eastern coast of Numenor. All the others were in use by the king's army. These ships were the ones belonging to the remaining Faithful. These ships contained the people who founded Arnor and Gondor, as well as a seedling of the white tree and the seven palantir, gifts of the Eldar to their ancestors.
The two main characters in this part were Jeremy and Alwin, standing at the window. In an earlier version, Jeremy calls Alwin Elendil. The significance of this is that in both the Lord of the Rings and the Alkallabeth, Elendil is the leader of the Faithful, and the king of both Arnor and Gondor. Elendil was also the father of both Isildur and Anarion. While in the Notion Club Papers, no sons are mentioned, as nothing is mentioned directly, The Lost Road, has only one son mentioned and he was not named Anarion or Isildur. Though the idea of having Jeremy call Alwin, Elendil was discarded, I think that the idea was none the less still in Tolkien's head as he wrote the next version, just from the style of the dialogue.

The storm Tolkien used to portray the downfall of Numenor started in the middle of the Atlantic, and continued eastward diminishing in strength like a tidal wave. This is reminiscent of how the storm cause by the Valar as part of the Downfall would probably have acted along with the changes caused by bending the world from a flat plain into a sphere, while simultaneously removing a portion of it.

One theme that recurs in both the Notion Club Papers and in the Return of the King, is that of a dream of a great green wave overtaking the land. (Tolkien himself is said to have had this dream several times) In the Lord of the Rings this dream is given to Faramir, and shows up at the moment the Ring goes into the flames in the Cracks of Doom. He is telling it to Eowyn. In the Notion Club Papers the theme occurred several times in the first part as they were talking of dreams.
Another common theme in The Notion Club Papers and The Silmarillion is that of a green land with a tall mountain with a name meaning "Pillar of Heaven". In the Notion Club Papers, it is Minul-Tarik while in the Alkallabeth it is the Meneltarma.

With some other clues during the storm, I think that somehow Ramer, Alwin and Jeremy were descended from the Numenoreans that escaped the downfall. From the tone of what was said, it is possible that Alwin and Jeremy were descended from Elendil and that the view of what was happening was from Elendil (Alwin's point of view) and either Isildur, Anarion or whoever was Elendil's son at the time of writing The Notion Club Papers (Jeremy). I don't think that Ramer had the pure blood of Numenor, though he probably had a good share, because he wasn't reliving the downfall, though he did have some understanding of what was happening and he was affected by what was happening. I do not think that any of the other members of the club were of Numenorean descent at all as they had no understanding of the events or any feeling for what was happening.
Alwin and Jeremy left the rooms during the storm and later sent a letter from somewhere unknown (the postmark was obliterated) on the west of England I think from the names used. This seems to me to be like the escape of the ships from Numenor.

When they arrive back in Oxford, for the next meeting, Alwin and Jeremy start to tell of the events since the storm. At this point there is an amazing similarity to The Lost Road.

Earlier I told of my theory that Alwin's father took the "Straight Road", well the first of their dream "hosts" (see part one of the Notion Club Papers for an explanation of this) was a man who's father had been a sailor and with a ship called the Earendel that had also disappeared without a trace. The dream "host" had lived in the time of the Danish invasion of England Taken from Christopher Tolkien's notes, this Eadwine was about 45 years old at the time. Christopher Tolkien got this information from historical references in the manuscript. Alwin was about 48 during the eventful meetings of the Notion Club in the story, so there were several similarities between the two men. Possibly Eadwine was an ancestor of Alwin. Another similarity that goes with the voyages is that, Earendil took ship with the last of the Silmarils with three crew and never returned to Middle-Earth, Alwin's father possibly found the "Straight Road" again with three crew, in a ship called the Earendel, Alwin's dream "host's" father disappeared in a ship called the Earendel though there is no mention of the number of crew, and Elendil's father Amandil took ship into the west with three crew. Now if there is somehow a connection with Elendil in Alwin's mind, perhaps his father had the same connection with Amandil, and Eadwine had the same connection with Elendil.
Aelfwine and his friend Treowine (Jeremy) set sail in a lone ship with no other crew. As they leave the coast they see the trademark cloud eagles, at which point Aelfwine says something about the downfall of Numenor and the ship sails to the west with a good east wind. Treowine sees the earth sink below them and they come to see the Undying Lands. This is the point that the manuscript breaks off.

Later in Sauron Defeated there are earlier versions of the manuscript in which the two languages are not Quenya and Adunaic, but Quenya and Sindarin.

This has the same general theme as the Notion Club Papers and is also unfinished. This time instead of Numenor intruding in dreams, the main character travels back in time with his son, in steps, much like where The Notion Club Papers manuscript breaks off.

The beginning of the Lost Road is very similar to that of the Notion Club Papers, with fragmentary "echoes" of the Elvish and Adunaic tongues entering through dreams. The main character's name has links with the name Aelfwine, much the same as in the Notion Club Papers. According to Tolkien the name Aelfwine means Elf-Friend.

In the Lost Road, there are two languages coming through. One of which the main character calls Berilandic (which later in the Lord of the Rings and The Silmarillion becomes Sindarin) and one which though no names are given, I think to be Quenya. The name it is given in the Lost Road is Eressean, which should say something as in the Silmarillion, Tol Eressea is the island on which many of the elves (with the people of the Vanyar being a notable exception) dwell, including a majority of the Teleri that heeded the Valars' request (with the others becoming the Dark Elves) and the High Elves or the Noldor. The name for the Elves that returned from the Undying Lands with Feanor, against the will of the Valar, was also High Elves or the Light Elves, having seen the light of the Two Trees. The Noldor made up a large portion of the elves that left and the language of the Noldor was Quenya, so the language of the high Elves was Quenya.

One of the themes in both the Notion Club Papers and The Lost Road is that of the "Straight Road", that exists to the Undying lands that are no longer a part of Middle-Earth. As all of Middle-Earth is now bent in the form of a globe, the "Straight Road" is the only way to reach the Undying Lands, and normally only the special ships of the Elves can navigate it. There are exceptions, which Tolkien admits to at the end of the Alkallabeth, in the Silmarillion.
It is most common for a mariner who finds the "Straight Road", to move far enough along to see, the Undying Lands with the spectacular sight of Taniquetil, the mountain of Manwe, before they die of lack of air. Though extremely rare, it is possible that some of the mariners actually make it to the Undying Lands.
While in the Notion Club Papers, there is a strong interest in dreams, in the Lost Road, the main character expresses a strong desire to go back in time.

Tolkien has used almost the same verse in both the Lost Road and the Notion Club papers. The verse is (copied from The Lost Road):

Then there is a gap and the second part is a lament

The Lost Road translation

The gap

My translation will have italics for the names otherwise it is in plain text:

The Gap

The wording is different in the Quenya and Andunaic versions in the Notion Club Papers but the translation is essentially the same. What the verses are is the first part is an account of the downfall of Numenor and the second part is a lament of the fact that there is no longer an Uttermost West in which the Undying Lands were as the Undying Lands were no longer a part of Middle-Earth.

In The Lost Road as in The Notion Club Papers, references to Numenor and to the Eagles of the Lords of the West slip through, though neither Alboin or Alwin really understand them or remember that they were saying them. Again in the Lost Road as in The Notion Club Papers there is one person who sees the silent scenes and one who hears the words with no pictures associated. In this story the person who sees the pictures is Alboin's son Audoin, while in The Notion Club Papers, Jeremy and Alwin are totally unrelated.

In both the Lost Road and The Notion Club Papers, Tolkien has used many historical references, though it is especially apparent in the Lost Road as far as it gets.
Much of the early part of the tale was set in Numenor, with Elendil talking to his son (as I mentioned earlier, at that time Elendil only had one son, in this story named Herendil) about the history of Numenor before the coming of Sauron. At the beginning of this part of the story Herendil was found lying on a stone wall thinking, which is how Alboin found his son at the beginning of the story. The story ends here though there are several rough pages with ideas.
The idea of having Numenor at the beginning was so abandoned and Numenor was placed at the end of the story.

The manuscripts leading up to the Alkallabeth which is the only finished Numenor story and any comparisons between them and the previous two (The Notion Club papers and the Lost Road) are in this section.

Apparently the final scene in the Lost Road is what survived in the Alkallabeth as the Downfall of Numenor.
At the same time as Tolkien was writing the earlier versions of the downfall of Numenor, he was working on the Quenya languages. This was also at the time he was working on the Lost Road, so at the time he had also expressed a desire to rewrite the Atlantis legends. I guess it is a bit of a coincidence that the word "atalante" was used to mean "she-that-has-downfallen". Perhaps the reason is that he was doing them at the same time.

The Fall of Numenor is earlier than the Lost Road as can be told by the names Tolkien used, In the earlier stories, Sauron was named Sur and Tarkalion was Angor. Though the Fall of Numenor is earlier it is probably only very slightly earlier than The Lost Road, as Tolkien was still developing the name "Numenor".
These two manuscripts are later than the manuscripts for the Quenta and the Ambarkanta though as both The Lost Road and The Fall of Numenor use the term Middle-Earth and neither of the two before mentioned do until the Annals of Valinor.
It seems that the idea of Numenor came from a conversation with C.S. Lewis. Another name for Sauron is Thu. This name is used in The Fall of Numenor, and some of the other early manuscripts.

In the Fall of Numenor and the Drowning of Anadune, the long life of the Numenoreans is given to the fact that they were allowed to sail to Tol Eressea, though this is very clearly not so in the Alkallabeth. In both the Fall of Numenor and the Drowning of Anadune the ban is to go farther west than Tol Eressea while in the Alkallabeth it is to go more than a day's sailing west of Numenor.
In the second version of the Fall of Numenor, the mariners were still permitted to sail to Tol Eressea and no further, but the Numenorean Kings were permitted to sail to Valinor once before they were crowned. This is an extreme difference from the Alkallabeth. The long life was still ascribed to their nearness to Valinor though.
Paragraph 6 of page 15 in the book The Lost Road is almost the same as the same paragraph in the Alkallabeth, describing the ships with which Tarkalion or Angor was attacking Valinor.
In the Fall of Numenor Tolkien had the rift created by Manwe destroy both Tol Eressea and Numenor. In the Alkallabeth the rift was east of Tol Eressea and destroyed only Numenor, while in the Fall of Numenor the rift was west of Tol Eressea and destroyed both.
In both the Alkallabeth and the Fall of Numenor, the survivors of the downfall were desiring long life and the tombs were more splendid then where the living were, and men looked for how to increase lifespan. The concept of the "Straight road" was very firmly established in the Fall of Numenor as in the Alkallabeth, the Notion Club Papers and The Lost Road. It was in the Fall of Numenor that the names Numenor and Andor (The Land of the Gift) first came about, that are used in the Alkallabeth. A mistake in the Alkallabeth is the mention of the Gates of the Morning, because they were eliminated in the Silmarillion and not needed in either the Fall of Numenor or the Alkallabeth but were not removed from either one.

At the time he was writing the Fall of Numenor, Tolkien had only one son of Earendil, not the twins as in the Silmarillion and the Alkallabeth.

In the Fall of Numenor, as in the Alkallabeth, Tolkien had the Numenoreans become more like the elves, eg. taking on their language. In the third version of the Fall of Numenor, the part about the kings being able to land once each lifetime in Valinor was removed, but the ban still extended to allow the Numenoreans to land on Tol Eressea.

At first Tolkien was using the end of the Fall of Numenor for part of the Council of Elrond as it was told in the Treason of Isengard which is the 7th book of the history of Middle-Earth series.

The part about the last King of Numenor sending his servants to fetch Sauron is almost the same as in the Alkallabeth.
For the most part, the Fall of Numenor remained in a very brief outline form all the way through its versions, with parts being moved to the Lord of the Rings, which shows that this was written in the late 1930's to 1942 which was when certain changes were made in the Lord of the Rings that made changes necessary in both works.
While the Fall of Numenor was written with the Lost Road in mind, the manuscript of the Drowning of Anadune was written for the Notion Club Papers. In fact Tolkien used the end of the Fall of Numenor in the chapter The Council of Elrond in the Treason of Isengard.

The beginning of the Drowning of Anadune starts with a brief history of Middle-Earth, whereas both the Fall of Numenor and the Alkallabeth start at the end of the wars over the Silmarils, with the Men who had helped the Valar overthrow Morgoth sailing to the island that was their reward.
At the time of the writing of the first manuscript of the Drowning of Anadune the idea of Numenor as a reward was either discarded or had not been decided on, as when Earendil sailed into the west looking for aid, the Valar say that they have not the right to make war on Morgoth, though they do raise an island that is called Numenor, for those of the Edain that have not turned to Morgoth.
Something I have noticed is that while in the Alkallabeth, the last king of the Numenoreans is called Tar-Calion, The Lost Road, The Notion Club Papers, The Fall of Numenor and the Drowning of Anadune all have his name as Tarkalion. Of course, early versions of other Quenya or Sindar names spelled with a "C" were spelled with a "K" example, Celeborn (as in the finished version of the Lord of the Rings) was originally spelled Keleborn, and is supposed to be pronounced as though it was spelled with a "K". I suppose that Tarkalion, later Tar-Calion is just another example of that.
The third version of the Drowning of Anadune is very similar to the Alkallabeth in many ways, some of which include: that death was no longer a peaceful drifting into the long sleep, but often came along with sickness and madness. The description of the temple that Sauron had built, except that it had a silver dome, not gold. The description of the charges that Tarkalion used as excuses to use the faithful for sacrifices.
The name "Elendil" has been used all the way through all of the stories that I have mentioned and been using in this comparison study and The Drowning of Anadune is no exception.
The idea of Amandil, father of Elendil, sailing into the west to betray Tarkalion's plan to the Valar is told in almost the same words as in the Alkallabeth, with the main exception being that Elendil's father's name is Amardil in the Drowning of Anadune. The Drowning of Anadune is very similar to the Alkallabeth with the main exception being different names etc. up to the point of Tarkalion's ships surrounding Tol Eressea. In The Drowning of Anadune, Tolkien has both Tol Eressea and Numenor destroyed by the chasm Iluvitar created between Tol Eressea and Numenor, while in the Alkallabeth only Numenor was destroyed and the whole of the Undying Lands was removed from the circles of Arda.
The Drowning of Anadune is the most likely ancestor of the Alkallabeth according to Christopher Tolkien (Sauron Defeated page 353) and I agree, from reading the two works simultaneously.

The Alkallabeth: I skipped the last version of the Drowning of Anadune as there is almost no difference from the Alkallabeth except for the following:

1. Peoples names
2. The fact that in the Drowning of Anadune there is no real distinction between the Valar and the Eldar.
3. Some place names are different from the Alkallabeth.

In the last version of the Drowning of Anadune, Earendel gains the name used in the Alkallabeth, Bright Earendel.

In the Alkallabeth though not in any other of the stories used here, Elrond, has a twin brother Elros, who is the first king of the Numenoreans, not Elrond as is in the other versions. Also while Elrond chooses to have the life of the Eldar, Elros chooses the life of the Edain, though he was granted a life span many times greater than any other of the Edain.
While in the Drowning of Anadune the Numenoreans only became tyrants on Middle-Earth during the reign of the last king, Tarkalion, in the Alkallabeth it first happened during the reign of the thirteenth king, Tar-Atanamir.
The names of the Numenorean kings are almost the same in all of the versions that I have read, but with one difference, in the Alkallabeth, the kings used the various tongues of men, so the last king's name was Ar-Pharazon, usually called "The Golden". All else is virtually the same between the Drowning of Anadune and The Alkallabeth.