Given Lisp, I can implement a Lisp interpreter easily:

    (loop (print (eval (read)))

Yes, but can you write a standards-compliant C++ compiler?

Easily, because in bizarro-one-language universe, I also have an infinite supply of monkeys. Hah!

Put one monkey to work on C++ and assign the rest on Hamlet. Oh, and make the C++ one use a typewriter too.

I think that compilers should be specially easy to write in Lisp over any other language.

However in the time that most people were writing compilers no common or popular computer had enough memory to run Lisp reasonably. Even 8MB were a luxury.

Now we have 2GB of RAM as the norm.

As I replied to ca above, this would be breaking the single rule in question. You are limited to a single language, not a single compiler/interpreter to start with.