CL is very much a general-purpose language. The PCL book (see CL forum's FAQ) is a good online source to read.
What will you learn from CL? IF statements can return values, regular syntax means you don't have to write parsers for custom languages and data files, real macros can be so much nicer than cpp macros and C++ templates, multiple dispatch is awesome, interactive programming doesn't mean you need a slow/interpreted language, dynamic variables are halfway between lexical and global variables, anonymous (lambda) functions are really useful, etc.
I would also recommend taking a look at
Racket. It is a Scheme, not a CL, but it is much more featureful than most Schemes and it has a strong user community.