The solution is far from simple if you want to do it in 100% Common Lisp as there's no CL HTTP client that can verify certificates. Maybe possible with drakma and cl+ssl and a custom configuration of the latter and a native OpenSSL library, and I still have doubts.
That is shocking! I do not know well the common lisp community. Am I write in thinking that racket has an http client that can verify certificates or am I underestimating the complexity of ssl?