Aye, but C.S. Lewis (like Bertrand Russell) constructs arguments that are fundamentally flawed in many places. They are lovely seductive arguments (hence why they are oft-referenced), but they are not rigorously correct arguments and could be taken apart by someone already well-studied on the topic. C.S. Lewis uses specious reasoning that does not cut it for rigor, so I would generally not recommend using that to convince a knowledgeable, rational, and intelligent atheist. Quite honestly, C.S. Lewis makes me cringe precisely because there are so many transparent flaws in his reasoning.
By far the most rigorous theologian on the rationality of Christianity is William Bartley, most famously in his book "The Retreat To Commitment". While the book is not written as a truly rigorous construction, others have shown that it can be written up as a rigorous construction in a mathematical sense (something with which I concur). Because of this, it is well-received by atheists since most will be able to follow the correctness of it from first principles. C.S. Lewis et al make unreasonable assumptions in their arguments, which is why many atheists reject the arguments.
So, nix the C.S. Lewis and go with W.W. Bartley. It is your best shot for the well-educated, intelligent, and rational.
Thank you very much for the reference to ""The Retreat To Commitment". I hadn't heard of William Bartley's book before.
Best regards
Examples?