Given that GP said "cross-platform" and then separately "possible derive mobile", I'm guessing that only supporting OS X on the desktop might not be enough for them. That being said, I'd be very surprised if there weren't cross-platform desktop GUI libraries available for Common Lisp.

I'd be shocked if WxWidgets weren't supported, maybe even Qt.

Interesting, but premise seems to be that UI code should be done outside of Lisp. Whereas, at least in my experience, this is where most code and trouble lives.