Tolkien, on Lewis' conversion to Christianity, was reportedly disappointed that Lewis preferred the Anglican denomination to Tolkien's own Catholic faith. read more
You can get details from"The Inklings: C. S. Lewis, J. R. R. Tolkien and Their Friends" by Humphrey Carpenter. He mentions some internal tensions, and Tolkien disapproved of Charles Williams and his influence on Lewis. But nothing that could be called a"falling out". read more
Tolkien helped return Lewis to the Christianity of his youth, whereas Lewis encouraged Tolkien to expand his fictional writing; both taught at Oxford and were members of the same literary group, both were interested in literature, myth, and language, and both wrote fictional books which propagated basic Christian themes and principles. read more