I would have picked something by william lane craig,richard swinburne or alvin plantinga. I mean mere christanity if i remember right is the book where he brings up the triliema argument for the jesus being god.
Lewis doesn't argue that the trilemma proves Jesus was God - he uses it to dismiss the wishy-washy agnostic position of "Well, Jesus was a great moral teacher, and worthy of respect, so whether he was God or not doesn't matter."
Lewis' position is "No, hang on a minute, this is someone who's spouting moral platitudes that everyone already agrees with, not anything new as far as the morals go. But he's also claiming to be God - he's saying, over and over again, that he is God. That leaves only three options, really - either he's actually God, or he's a liar, or he's deluded. Whatever he was, he wasn't an exceptionally decent human being, so get off the fence."
In an Open Thread comment beriukay mentioned that he's reading C.S. Lewis' Mere Christianity. I've been reading it too, for interesting reasons.
In my case it so happened that I started discussing faith with a long-time online friend whose spiritual views I didn't yet know, and he turned out to be a Christian with a high regard for the Bible, who also has an interest in science. As our discussion turned to our readings on spirituality, I acknowledged (I think it was me) that I probably spent more time on books that reinforce my point of view than on books that challenge it, perhaps a case of confirmation bias. (I've been exposed to many poor arguments for Christianity, and dismissed them; but possibly that was largely a function of having started out with that bottom line already written and picking arguments I wouldn't have much trouble refuting.)
In the spirit of experiment we agreed to a "trade" - he would read (thoughtfully and with an open mind) a book of my choosing on reasons to doubt faith, and I'd do the same with a book he chose on Christianity.
So the idea here is to pick a book that's the "best argument from the other side" (as in quote 3 here).
I recommended The God Delusion - I'm not sure if that's the best choice given the above intent, but it's what came to mind on the spot.
Would you make a different choice? If so, what?