You say Lewis and Tolkien argued about mythmaking. What about?
If you read his poem "Mythopoeia," Tolkien's position is that Nature is the book of God. You can read Nature the way you could read a book and that myth is the same way. It is full of a kind of neo-Platonism. You can hide Christian truth in it. Lewis had a much more empirical view of the real world. He didn't see anything wrong with adding Christian references to his fantasy, which is why the Chronicles of Narnia have specific references. The difference was in the esthetic. Their theology was of course different: Tolkien was a Catholic and Lewis was an Episcopalian.

Lewis might have regarded a tree as just a tree. For Tolkien, a tree was alive with meaning of all sorts, not only an embodiment of all the vitality of the natural world, but it might also represent, say, the force that Tom Bombadil represents in the Fellowship of the Ring. Some sort of principle of creation. It has within it the idea of a tree, treeness, and then also more symbolically trees represent the Cross. Just as Limbas, the golden food that lasts for days and keeps you whole is like a communion wafer.

You have a chapter on difference in your book. What's important about how Bilbo and Frodo are different from other hobbits after their adventures?
At the beginning of the trilogy, Bilbo doesn't seem to age, and that seems queer to the rest of the hobbits. But what makes him queer-I don't mean in the slang sense, but different-is that he has been stretched. He has a sensitivity to moral issues that he has gained from carrying the Ring for so many years, and having to resist temptation. To be a good person is to be queer, the way a saint is queer.