You mean a toy LISP or Scheme? Any serious LISP system uses a compiler. It compiles and runs strings. The "eval" creates native binary executable code.

No decent-performing system totally skips compilation. You just don't notice that it is happening. Even a web browser compiles the javascript before running it; that is what a JIT does.

I mentioned the syntax "(+ 1 1)" because you're trying to disqualify C++ homoiconicity on a superficial syntactic basis. If you can do that, then it is equally valid to say that LISP can't do simple addition.