There are some implementations that compile to C code, e.g. ECL (Embeddable Common Lisp). There is also a very recent library that compiles a subset of Common Lisp to a subset of C++ for the Arduino.
You mentioned "real-time" so nonchalantly, but getting real-time with garbage collection is not trivial. There do exist real-time garbage collectors, but I am not aware of any Lisp implementations using them yet.