That depends on what you mean by "purely functional Lisp". You can write purely functional code in any Lisp, and you can compile any Lisp to machine language, and this has been true for decades. AFAIK there is no Lisp that enforces purely functional programming, but it's easy to build one if that's what you want.

That is what I want.

Turns out that LFE (Lisp-Flavored Erlang) exists…

Wait, doesn’t Clojure have this, to a large degree at least?