I love Common Lisp, but I would definitely think twice before implementing anything I want other people to use on their machines in it. A tiny C executable is pretty nimble in comparison to anything you'll get out of Common Lisp.
Assuming everyone has a CL installed is going to limit the audience pretty drastically.
And what about dependencies? Assume they have quicklisp installed as well?
Like I said, I love Common Lisp, but every language is some kind of compromise.