I wrote a lisp, a while back, and then later added an LSP for it.
Since lisp is so simple in terms of syntax what I really did was tab-completion, and info-on-hover, for the built-in functions like "car", "cdr", and the primitives I added as part of a more complex standard-library.
In my case I was writing in go and I found an LSP-server package which was trivial to use. So getting the integration with emacs, vim, etc, was really trivial:
