CLISP is just one implementation of Common Lisp. It's a very good implementation, and it does have some support for being embedded in other (C-based) programs, but that's not its focus and it's GPLed, which may or may not be a deal-breaker for you.
You might be interested in checking out ECL. This implementation is specifically designed to be embedded (indeed, the "E" stands for "Embeddable"!), and has numerous features that might be useful to you, including the ability to compile Common Lisp programs to C (as well as providing byte-code compilation and an interpreter).