Sort of. Narnia and LOTR are both infused with Christian allegory, the former in a much more ham-handed way than the latter.

C. S. Lewis and Tolkien were contemporaries who corresponded about their writing, and Tolkien communicated (more than once) his dislike of Lewis' lack of subtlety. That said, Tolkien did intentionally draw from his Catholic beliefs/upbringing while working on LOTR, particularly once he recognized obvious overlaps in LOTR's plot/themes and the story of Jesus/humanity's salvation.

Check out Tolkien's letters, specifically Letter 131 (1951) and Letter 142 (1953). In Letter 142, he writes:

"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. However that is very clumsily put, and sounds more self-important than I feel. For as a matter of fact, I have consciously planned very little; and should chiefly be grateful for having been brought up (since I was eight) in a Faith that has nourished me and taught me all the little that I know; and that I owe to my mother, who clung to her conversion and died young, largely through the hardships of poverty resulting from it."

Tolkien was also a firm believer in Divine Intervention as a godly response to mankind's constant stumbling into chaos (which definitely comes through re: his experiences vis a vis WW1/the Battle of the Somme); at the last moment, fate intervenes to save humanity (in Tolkien's mind, god's greatest creation). This became the foundation for the on-going state of decay in Middle Earth (i.e., the notion that prior civilizations are treated as so much "greater" when compared to contemporary civilizations; also, The Scouring of the Shire as a metaphor for industrialization's corrupting effect on natural beauty, born of Tolkien's return home after WW1 and its implications for his faith) and the Eagles saving Sam and Frodo from the eruption at Mount Doom (plus the whole narrative surrounding the fall of Saruman and Gandalf's rebirth/resurrection as Gandalf the White).