Although Tolkien famously discouraged allegorical readings of his books, it's not a stretch to say that at least some of the imagery and symbolism came from his devoutly Catholic lifestyle. Tolkien himself admits this in Letter 142 (emphasis mine):
The Lord of the Rings is of course a fundamentally religious and Catholic work; unconsciously so at first, but consciously in the revision. That is why I have not put in, or have cut out, practically all references to anything like 'religion', to cults or practices, in the imaginary world. For the religious element is absorbed into the story and the symbolism.
The Letters of J.R.R. Tolkien 142: To Robert Murray, SJ. December 1953
This isn't an altogether uncommon reading, either. In Letter 213, in response to questions about himself, Tolkien writes (emphasis mine):
I am a Christian (which can be deduced from my stories), and in fact a Roman Catholic. The latter 'fact' perhaps cannot be deduced; though one critic (by letter) asserted that the invocations of Elbereth, and the character of Galadriel as directly described (or through the words of Gimli and Sam) were clearly related to Catholic devotion to Mary.
The Letters of J.R.R. Tolkien 213: To Deborah Webster (Incomplete). October 1958
Tolkien's phrasing in the above letter indicate that he doesn't put a lot of faith in this reading1, and in Letter 269 he expands on that belief:
I don't feel under any obligation to make my story fit with formalized Christian theology, though I actually intended it to be consonant with Christian thought and belief
The Letters of J.R.R. Tolkien 269: To W. H. Auden (Incomplete). May 1965
Notes in some of his other writings also indicate that Tolkien was unhappy with the results of borrowing too directly from Catholic theology. Darth Melkor discusses this in an excellent answer to a related question; Tolkien had noted the similarity between his conception of Eru Ilúvatar and the Catholic Trinity, and was very unhappy about it.
For all his devout Catholicism, Tolkien was unsatisfied with the idea that British myths needed to reflect the moral sensibilities of the modern world2, as he wrote in Letter 131 (emphasis mine):
Of course there was and is all the Arthurian world, but powerful as it is, it is imperfectly naturalized, associated with the soil of Britain but not with English; and does not replace what I felt to be missing. For one thing its 'faerie' is too lavish, and fantastical, incoherent and repetitive. For another and more important thing: it is involved in, and explicitly contains the Christian religion.
For reasons which I will not elaborate, that seems to me fatal. Myth and fairy-story must, as all art, reflect and contain in solution elements of moral and religious truth (or error), but not explicit, not in the known form of the primary 'real' world.
The Letters of J.R.R. Tolkien 131: To Milton Waldman. 1951
Remember that Tolkien's goal was to create a mythology for the British people; the ancient British wouldn't have had a notion of Christian values, because Christianity wouldn't have been a thing. Rather than attempting to exactly duplicate the existing parables, Tolkien took the import elements and re-worked them into something recognizably related, but distinct. He writes about this briefly in the unsent Letter 212 (emphasis his):
I suppose a difference between this Myth and what may be perhaps called Christian mythologyis this. In the latter the Fall of Man is subsequent to and a consequence (though not a necessary consequence) of the 'Fall of the Angels': a rebellion of created free-will at a higher level than Man; but it is not clearly held (and in many versions is not held at all) that this affected the 'World' in its nature: evil was brought in from outside, by Satan. In this Myth the rebellion of created free-will precedes creation of the World (Eä); and Eä has in it, subcreatively introduced, evil, rebellions, discordant elements of its own nature already when the Let it Be was spoken. The Fall or corruption, therefore, of all things in it and all inhabitants of it, was a possibility if not inevitable.
The Letters of J.R.R. Tolkien 212: To Rhona Beare (Draft). Unsent.
A particular example is one of the ones cited in the question: the downfall of Númenor. Although there are some similarities between that story and the story you mention, and more directly to the story of Noah and the Great Flood, ultimately Tolkien intended it to be his version of the Atlantis myth. He makes the parallel frequently in his letters, but the one I'm going to quote comes from Letter 154:
The particular 'myth' which lies behind this tale, and the mood both of Men and Elves at this time, is the Downfall of Númenor: a special variety of the Atlantis tradition. That seems to me so fundamental to 'mythical history' – whether it has any kind of basis in real history, pace3 Saurat4 and others, is not relevant – that some version of it would have to come in.
The Letters of J.R.R. Tolkien 154: To Naomi Mitchison. September 1954
1 Although he softened on this particular case later in his life; in Letter 320 he wrote:
I think it is true that I owe much of [Galadriel] to Christian and Catholic teaching and imagination about Mary
The Letters of J.R.R. Tolkien 320: To Mrs. Ruth Austin (Incomplete). January 1971
2 In fact there's a case to be made that The Lord of the Rings is itself a reaction against modernization. But you could write a book on that subject, which I'm not going to do here
3 "With all due respect to"
4 Likely a reference to Denis Saurat, who wrote a book called "Atlantis and the Giants", which barely exists online. Near as I can tell from references to it, Saurat wrote the book based on the premise that Atlantis was a historical fact