Mere Christianity is an intellectual "proof" of the truth of Christianity. Now you would probably think that as I believe the truth of Christianity I would be right in that book's wheelhouse. However, I was not.
The problem was that lewis arrived at conclusions with which I disagreed because his best tool was to create artificially restrictive dichotomies. He would say "it is either x or y, and since it cannot be x it must be y" while I would think, "but what about a, b, and c."
That being said, not a bad book and there is plenty to give people to think about how to be a better person. A lot on treat others well and don't judge someone because you can't know where they are coming from, which is a good idea for everyone regardless of faith.