'...the Person never named...'
Tolkien was a complex person. Some of my favorite places in his letters are where we see two different sides of him in close juxtaposition. In a letter written in 1956 (Letter #192), he mentions a reviewer's comment that although God is never named in The Lord of the Rings, God's presence is never absent. Tolkien seems happy about the comment, glad that some people, at least, are aware of the religious foundation of the story. But then he seems compelled to add, in pure professorial style (in a footnote, no less), that, of course, to say that God is "never named" in LotR isn't precisely correct, as Eru is referred to as "the One" in Appendix A. So, with that exception in mind...
Since Middle-earth is meant to be part of our own world thousands of years ago, and because Tolkien is a believing monotheist, he doesn't take the liberty of inventing a new God or gods for his secondary creation. He doesn't add a parallel to Christ, since that would mean the Incarnation of Jesus wasn't unique.* As is clear from the footnote in the letter mentioned above, as well as from other statements in his letters, Eru is God, that is, the God of Abraham. In The Silmarillion, God is spoken of by two titles: Eru (the One) and Ilúvatar (Father), indicating the same kind of relationship with his creatures that we recognize today: He is completely Other, but totally intimate.
The Silmarillion, though, gives a broad sweep of history, beginning with a creation story that involves the Ainur, angelic-type beings who know and serve Ilúvatar. In LotR, we're in the much more limited world of Middle-earth at the end of the Third Age. The concept of a personal God seems to be missing.
Tolkien never tells us when his stories of Middle-earth take place, and he never ties them in with external, primary-creation history. To make it "work" for myself, I think of the Third Age as occurring after the Tower of Babel but before Abraham (I want to stress that I'm not in any way saying it was Tolkien's intent to place it at that time - more on that in the next essay - it's just a thought that works for me). In Tolkien's subcreation, Men had known something of God, but when Númenor was destroyed (because of Men's overweaning pride, somewhat like the Tower of Babel) much of that relationship was lost because the mountain that was the one place to worship the One was gone. Tolkien compares the result to the destruction of the Temple in Jerusalem, but it is even more extreme. For the Jews, because sacrifice could be performed only in the Temple, the destruction of the Temple also destroyed the practice of offering sacrifice. With the loss of their place of worship, the Númenoreans felt they could no longer even worship Eru. The closest thing to worship that we see among the descendants of the Númenoreans in LotR is the standing silence before a meal. They believe in what "will ever be," but can only reflect and remember, not truly worship or pray. A sad picture of a people in self-imposed exile from their God.
Some Tolkien readers think the hobbits' lack of religion is so strange that they give the Shire church buildings in their fanfic. Is it so strange? Hobbits' original exposure to such staples of civilization as reading, writing, and building seems to have come primarily from the Dúnedain, who felt they no longer had a relationship with Ilúvatar. How could they teach another people about Him? Because of this lack of teaching by Men, the hobbits who do have an understanding of what we might call spirituality have learned it from the Elves; specifically, Bilbo learned it from the Elves and passed it on to Frodo and, to a lesser extent, his younger relatives and Sam. So when Frodo needs protection he doesn't call on Ilúvatar but on Elbereth (even using the same name for her that an Elf would).
But, the other side of the argument continues, all cultures have something akin to religion; there seems to be something built into the makeup of human society that needs an ultimate framework on which everything else depends. If hobbits didn't learn religion from the Dúnedain, wouldn't they have come up with their own? They probably would have, and I believe they did - called "family." The importance of family history and the detailed customs and practices surrounding the extended family was the framework on which everything else in Shire society depended. We'll talk more about that in a later essay. In addition, if we look at LotR from the outside - as a work of fiction - we see that the Shire is based largely on the Edwardian England of Tolkien's youth, which was, after all, primarily a secular society with religion often being seen as simply part of someone's social obligation. In the Shire, that social obligation is more openly centered in family connections; the Shire's lack of organized religion is perhaps more honest than the part religion played for much of Edwardian society. Of course, in both societies there were people who were truly spiritual. In the Shire, Tolkien tells us to think of them as unusual rather than typical; I'm not sure how he would have asked us to think of the same type of person in the England of his youth.
The other half of the reviewer's comment, though, is that God is ever-present in LotR. The title of this section of essays is taken from a reader who wrote a letter to Tolkien commenting that faith shines through the story like "light from an unseen lamp." That this reader was not, at the time he read LotR, a believer, says some important things about the book, its author, and how the author wanted people to approach it. First, LotR was not written as a Christian book to be read primarily by Christians, or with the primary purpose of bringing people to Christ; the author made the point repeatedly that LotR is not an allegory but a story, showing what he believed would happen "if such a thing [as the Ring] existed." (Letter #109) That so many people find allegory in LotR where none exists, Tolkien might say, simply shows that the story does a good job of getting at the truth of "what would happen..."
And a major part of that truth is Tolkien's assumption that God is present and active at all times. Some critics have said that Ilúvatar is distant and uninvolved. But if we look at the action of Providence, and at the other ways that God is ever present in LotR, I believe we have to say that this distance and separation is only the perception of the people of Middle-earth - because they haven't yet learned to perceive Him any other way.
*This is in contrast to, for example, C.S. Lewis's Narnia, which is set up to be a different world from ours, although you can reach it from here. Because Narnia isn't our world, Lewis can give it Aslan as a parallel to Christ without giving our world two Messiahs.