How would it be run without Emacs?

You might point out that there are things like elisp.lisp that purports to run Emacs Lisp in Common Lisp, but I'm not sure that's viable for anything but trivial programs. There's also something for Guile, but I remain unconvinced.

Maybe a Common Lisp core with an Emacs frontend running it in https://www.gnu.org/software/emacs/manual/html_mono/cl.html?

Why not just use the best known emacs lisp core, then? Like say emacs.

To allow it to run on other lisp dialects as well.

(I’m just trying to defend GP’s point – I’m not a heavy lisp user myself, tbh.)

you could probably use the unexec tooling