They're compilers, not interpreters - or at least SBCL, CCL, ABCL, ECL, Clasp, CLISP, ABCL, and LispWorks are. I'm not aware of any other alive contemporary Common Lisp implementations.
Lisp is a memory-safe language with automatic memory management, which removes all of the aforementioned classes of attacks that are available in C. In addition, the Lisp compilers are written in Lisp itself, not in C, which further decreases the attack vector.
Also, the currently-in-progress SICL project intends to do away with C completely, even for its garbage collection and OS-interfacing parts.