At the same time, though, they also had serious disagreements--in particular, over the quality of Lewis' Narnia books--especially where the religious elements were concerned.
Christianity, Narnia, and Theology
Although Lewis was very proud of his first Narnia book, The Lion, The Witch and The Wardrobe, and it would spawn a massively successful series of children's books, Tolkien didn't think very highly of it. First, he thought that the Christian themes and messages were far too strong--he didn't approve of the way Lewis seemed to beat the reader over the head with such obvious symbols referring to and Jesus.
There was certainly no missing the fact that Aslan, a lion, was a symbol for Christ who sacrificed his life and was resurrected for a final battle against evil. Tolkien's own books are deeply imbued with Christian themes, but he worked hard to bury them deeply so that they would enhance rather than detract from the stories.
Furthermore, Tolkien thought that there were too many conflicting elements that ultimately clashed, detracting from the whole. There were talking animals, children, witches, and more. Thus, in addition to being pushy, the book was overloaded with elements that threatened to confuse and overwhelm the children for whom it was designed.
In general, it appears that Tolkien didn't think very much about Lewis' efforts to write popular theology. Tolkien seemed to believe that theology should be left to the professionals; popularizations ran the risk of either misrepresenting Christian truths or leaving people with an incomplete picture of those truths which would, in turn, do more to encourage heresy rather than orthodoxy.
Tolkien didn't even always think that Lewis' apologetics were very good. John Beversluis writes:
"[T]he Broadcast Talks prompted some of Lewis's closest friends to make embarrassed apologies for him. Charles Williams ruefully observed that when he realized how many crucial issues Lewis had sidestepped, he lost interest in the talks. Tolkien also confessed that he was not "entirely enthusiastic" about them and that he thought Lewis was attracting more attention than the contents of the talks warranted or than was good for him."
It probably didn't help that Lewis was far more prolific than Tolkien. While Tolkien agonized over The Hobbit for seventeen years, Lewis churned out all seven volumes of the Narnia series in just seven years, and that doesn't include several works of Christian apologetics which he wrote at the same time!
Protestantism vs. Catholicism
Another source of conflict between the two was the fact that when Lewis converted to Anglicanism, he adopted the Protestant Anglicanism instead of Tolkien's own Catholicism. This by itself need not have been a problem, but for some reason, Lewis further adopted an anti-Catholic tone in some of his writings which upset and offended Tolkien. In his very important book English Literature in the Sixteenth Century, for example, he referred to Catholics as "papists" and unreservedly praised 16th-century Protestant theologian John Calvin.
Tolkien also believed that Lewis' romance with American widow Joy Gresham came between Lewis and all his friends. For decades Lewis spent most of his time in the company of other men who shared his interests, Tolkien being one of them. The two were members of an informal Oxford group of writers and teachers known as the Inklings. After he met and married Gresham, however, Lewis grew apart from his old friends and Tolkien took it personally. The fact that she was divorced only served to highlight their religious differences since such a marriage was illicit in Tolkien's church.
In the end, they agreed on far more than they disagreed, but those differences--largely religious in nature--still served to pull them apart.
Cline, Austin. "C.S. Lewis and J.R.R. Tolkien Argued Over Christian Theology." ThoughtCo, Jul. 2, 2018, thoughtco.com/c-s-lewis-and-j-r-r-tolkien-christian-theology-249783.