I quite enjoyed learning Scheme at university. Coming from OOP, I loved when it just clicked and you began to look for opportunities to use higher order functions. I never actually used Lisp, so I might try that one with a small project.
For what type of web project could Common Lisp be a good fit? It should probably have something to do with huge lists of data that have to be processed, so that you can map, filter and fold them. The data should be relatively simple to obtain, too, so that the missing libraries are not that huge of a problem.