In Mere Christianity, Lewis gives this great little response to the so-called problem of evil.
If a good God made the world why has it gone wrong? And for many years I simply refused to listen to the Christian answers to this question, because I kept on feeling “whatever you say, and however clever your arguments are, isn’t it much simpler and easier to say that the world was not made by any intelligent power? Aren’t all your arguments simply a complicated attempt to avoid the obvious?” But then that threw me back into another difficulty.
My argument against God was that the universe seemed so cruel and unjust. But how had I got this idea of just and unjust? A man does not call a line crooked unless he has some idea of a straight line. What was I comparing this universe with when I called it unjust? If the whole show was bad and senseless from A to Z, so to speak, why did I, who was supposed to be part of the show, find myself in such violent reaction against it? A man feels wet when he falls into water, because man is not a water animal: a fish would not feel wet. Of course I could have given up my idea of justice by saying it was nothing but a private idea of my own. But if I did that, then my argument against God collapsed too- for the argument depended on saying that the world was really unjust, not simply that it did not happen to please my private fancies. Thus in the very act of trying to prove that God did not exist–in other words, that the whole of reality was senseless–I found I was forced to assume that one part of reality–namely my idea of justice–was full of sense. Consequently atheism turns out to be too simple. If the whole universe has no meaning, we should never have found out that it has no meaning: just as, if there were no light in the universe and therefore no creatures with eyes, we should never know it was dark. Dark would be without meaning.
C.S. Lewis, Mere Christianity, book 2, chapter 1, paragraphs 5-6.
To be fair, this answer in particular does not resolve the dilemma for the Christian. He or she is still left to grapple with the nature of evil within the Christian worldview itself. Since this worldview simultaneously holds to a God who is all-loving and all-powerful, the question then is, why does this God not eliminate evil? Lewis does not resolve that dilemma (at least here).
But, regardless of that, Lewis’ argument nonetheless puts the non-Christian, who has some sense of evil, on his heels. From where does that sense of evil, goodness, justice, morality, etc. arise? This is their (=the non-Christians’) problem of evil–within their framework: they cannot explain why a sense of evil persists.