Tolkien and Lewis were both deeply conservative (not Conservative), and represented a last, textual, gasp of the pre-Raphaëlite movement (for which they had both been born just a little too late).
And though they were friends, collaborators, and, as friends can be, competitors, there was one huge gulf between them: christianity. Tolkien loved and was a scholar of the pre-christian Sagas, which he felt were a deeply influential part of the English cultural underpinning. Middle Earth was a complex experiment in creating the Ursprung of that culture, but perhaps also a more English one.
While Lewis, upon seeing the success of The Hobbit, wanted to emphasize christianity as the core of the English culture. His novels, despite their settings (swords, no machinery, etc) and his conservatism, were very much 20th century in structure, sparseness, and the speed with which the plots developed: more Dorothy Parker than Thomas Mallory. But they were also unabashedly christian; deliberately not using christian vocabulary in an attempt to cast it as a universal truth.* In a way they were opposites.
* he was so convinced of the universalism of christianity that he simply presumed his readers would get it. Though I have spoken English all my life I had had no exposure at all to christianity when I read “The Lion, The Witch..” and so the whole scene where Aslan is killed, the stone table breaks and then aslan maybe returns just seemed strange and incomprehensible to me. I thought some pages must have been lost in a misprint of the book!