I wouldn’t get too caught up trying to find specific allegorical references in LOTR to the Christian story. As pointed out before Tolkien felt that allegory was an inferior story telling method, though he didn’t believe it was entirely without merit. He certainly didn’t write LOTR as Christian allegory, but that doesn’t mean he did not believe LOTR to be a thoroughly Christian work.
We have to look at Tolkien’s beliefs concerning myth to really understand how the LOTR myth could have related to Christianity in his mind. Though his thoughts about myth underwent some changes over his career and there can be found some contradictions in his works, his basic belief was that myth is a conduit to truth. He believed that all lasting myths hold their staying power in the fact that they relate some essential truth to humanity about life, the universe, and everything. The story form itself helped this revelation of truth as well, as opposed to say philosophical dissertation. One could write a dissertation or field a psychological study on human longing and anticipation, but the results could never be as relevant and moving as a good telling of the story of Orpheus leading Eurydice out of Hades and not being able to keep from looking back. His beliefs concerning myth were bolstered by the fact that so many myths around the world and throughout time contained similar characters and characteristics.
Tolkien went further than and suggested that Christianity is the uber-myth, the myth that all other myths were reflecting, were aspiring to be, because the Christian myth was the one myth that was literally true, historically, emotionally, philosophically. Thus he could believe that any myth, especially those that reflected the themes and characters in the Christian myth, were in a roundabout way a reflection of Christianity itself, myth being the way God reveals truth to humanity.
We can see reflections of Christian myth throughout LOTR. The title of book three should stand out immediately, as well as the archetype it is named after. I’m sure that Tolkien would believe that the last chapter of the Christian myth, which has yet to be written, will be similarly titled. We could write a book about the other Christian “reflections” found in LOTR, here a mere few:
The story of fall of man including Adam and Eve (Tom/Goldberry), and the redemption of mankind by a half-man/half supreme being.
The holy Eucharist, lembas bread’s healing properties, drinking from the common cup in Lothlorien.
The changing of history by God’s direct and divine interference in the world, causing the ring to find Frodo, sending Gandalf back from the dead until his job is done, etc.
Elbereth Gilthoniel, the queen of heaven, from whom the elves and other heroes of the book constantly ask for help is obviously a reflection of the Catholic beliefs and calls for supplication from Mary. (Some of the Elven and Catholic prayers are nearly identical).
We could go on and on but it is important again to say that he didn’t mean LOTR to be Christian allegory and therefore with all of its reflections of the Christian myth Tolkien still intended LOTR to be a story of its own and the Christian mirror was only one of many that he used to shine light on the creation of his story. Though he believed that in a roundabout way any good myth is a message from God, one myth in particular being God’s best story.