I had something like Lewis's experience when I presented a paper at Notre Dame on eliminative materialism. My commentator was Bill Ramsey, a UCSD graduate who actually did most of his work with Steven Stich rather than the Churchlands. In the exchange that ensued, I think the general consensus was that he had gotten the better of it. Did that tempt me to become an eliminativist? Certainly not. Did I ever cease to think that some kind of self-refutation argument could be made to work against eliminativism? No. But what it did show me was that I had failed to get fully "inside" the eliminativist perspective to be able to bring up objections that would draw iron. Ramsey subsequently published his reply in Inquiry, and I responded to that, I thought, reasonably well in that same journal. I also wrote another paper which came out in Metaphilosophy examining the eliminativism debate in light of an analysis of the fallacy of begging the question.
The overall reaction in the Oxford community might have been embarrassing and hard on Lewis. Lewis has said that one thing he didn't like about these Socratic sessions was that the credibility of Christianity seemed to hang on his performance in some particular debate. The fact that his adversary was young, female (Oxford in 1948 was less than fully converted to gender equality), and hitherto unknown didn't help. I take it when he later says "She obliterated me as an apologist" what he was saying was that he thought she had damaged his reputation amongst people who went to the Socratic meetings.
I know there was a subsequent discussion of the exchange between Lewis and Anscombe at the home of Lewis's physician Havard, who knew both of them. I'd give my eyeteeth for a record of what was said at that meeting. I also know that Lewis published a rebuttal in the Socratic Digest that same year. So if there was a time when he thought he actually thought the argument might have been refuted, it didn't last long.
Lewis came to reject naturalism in favor of absolute idealism as a result of an argument of this type in the course of his disputations with Owen Barfield prior to his conversion. However, if you read Surprised by Joy (and there is even more to the story than he recorded there), there were lots of factors in his conversion. It's unlikely that this would have triggered a crisis of faith.