I'm not an expert in Common Lisp internals, but there are some things that don't look like they could be entirely put in an executable without bringing the compiler and runtime along. I'm not just talking about things like a library that outright uses eval, but the more high-level things like macros that call compiled functions and reader macros.

Then again, you might be able to compile the compiler to LLVM IR -> emscripten -> JavaScript, and use that to compile CL code.