GOFAI type projects are a good way to experiment with Lisp, because the language's history and much of the literature before Practical Common Lisp are steeped in that kind of thing. Game playing, computer algebra, theorem proving, that sort of thing. If you really don't like that sort of thing, or want something more practical, tool-building is always fun. Generating Gtk bindings from gobject-instrospection metadata would be useful; generating X bindings from the XCB protocol descriptions probably less so but fun if you're into that sort of thing. Common Lisp's arrays are don't get much attention, but they're really well-thought out. Lisp doesn't have much of a reputation for numerical work, and it won't give you as much opportunity to play with the sorts of things people rave about Lisp for, but there's some cool stuff there you won't see in many blog posts. Writing a raytracer with a DSL for scene descriptions wouldn't be a huge project.