C.S. Lewis is often described as an "apostle" to the skeptics - that he somehow has a special affinity for the arguments, sensibilities, and perspectives of religious doubters and can therefore more easily reach them than other apologists. Lewis was himself an atheist for many years, after all, so it's understandable why this would make sense.
Of course, many apologists make a big show about how they were once atheists before finally seeing the light, so this doesn't entirely justify people's confidence in Lewis. He may appear to be directing his arguments to atheists, but the truth is that his arguments are primarily convincing to those who either already believe the conclusions or who are otherwise sympathetic to them.
This is revealed, at least in part, by the fact that Lewis demonstrates a great deal of hostility and arrogance towards nonbelievers. Lewis even refers to himself as having been a "fool" when he was an atheist, so it's difficult to imagine his regarding current atheists as anything else. Just in case there is doubt, however, John Beversluis has collected some of his numerous expressions of superiority:
"In Mere Christianity, for example, we learn that atheists are like ostriches: they keep their heads in the sand in order to avoid facing facts that damage their position. ...It is noteworthy that in Mere Christianity there is not one word about the "mixed" quality of the evidence for theism. Instead, those who have doubts about Christianity are ridiculed as pitifully unstable creatures who "dither to and fro" and whose beliefs are dependent "on the weather and the state of [their] digestion" (MC, 124). We are told that atheism is "too simple," that like materialism it is "a boys' philosophy," "a philosophy of the nursery" (R, 55). What is the implication of this if not that atheism and materialism are childish errors that are easy to refute and unworthy of the rational man?"
"...Turning to Surprised by Joy, we find that a young atheist "cannot guard his faith too carefully," that danger "lies in wait" on every side, and that a successful adherence to atheism depends on being very selective in one's reading (SbJ, 226, 191). We are again assured that atheism is a form of wish-fulfillment and informed that in its "modern" forms it has "come down in the world" and now "dabbles in dirt" (SbJ, 226, 139). Finally, we discover that atheists are not committed inquirers, that they merely "play at" religion, and that their minds reel "in a whirl of contradictions" (SbJ, 115)."
Lewis' comments are extreme to say the least, but what is particularly interesting is the almost total absence of any serious attempt to defend them. These are pretty serious allegations which Lewis is making. You shouldn't accuse someone of deliberately ignoring others' arguments or of "playing at" arguing without some serious evidence as support, yet you won't find any in Lewis' writings.
The above is just a sample of what Beversluis quotes, but you won't find these statements discussed by Lewis' many admirers. Why? Perhaps because Lewis is defending beliefs they already agree with. Perhaps they honestly don't have a problem with baseless ridicule of atheists whom they also believe aren't worth civil consideration. Skeptics notice them, though, and you don't reach religious skeptics by ridiculing them.
Thus, it's hard to defend the idea that Lewis really is writing for nonbelievers - or even intended to. It's more plausible that he was writing for believers and that the ridicule of nonbelievers helps create a sense of "us vs. them" solidarity among believers who have faith but don't realize that they have reason behind them as well. They can join together in pitying the poor, benighted atheists.
I had someone write to me defending C.S. Lewis and objected when I suggested that perhaps he found Lewis convincing because he wasn't familiar with the many logical flaws Lewis commits. This person found my suggestion personally offensive, but do you suppose he found any of Lewis' above comments offensive? I doubt it. When the suggestion of ignorance of a technical subject most people are ignorant of is "offensive," but accusations of intellectual dishonesty and instability are not, then you know that something is wrong.
Why does Lewis ridicule religious skepticism? In Surprised by Joy he is very up front about his motives: "The key to my books is Donne's maxim, 'The heresies that men leave are hated most.' The things I assert most vigorously are those that I resisted long and accepted late." Lewis "hates" atheism, materialism, and naturalism. His attacks on religious skepticism are motivated by religious passion, not by intellect and reason.