I use Awesome WM. It's essentially an "Emacs of Window Managers," and the codebase is very well written, with a small C core and everything else implemented in Lua. It's even very well documented. Yet, writing a nontrivial program (call it an "applet" or something) for Awesome is a nightmare compared to doing the same in Emacs.
LuaJIT is an excellent runtime, and Lua is a great IR, but writing it by hand for anything that's not strictly scripting within a previously established framework is challenging. It's to the point where I'm using Haxe to produce Lua for my Awesome scripts. I know a few people who use Haxe to script NeoVim, too. Really, having to reinvent inheritance and method resolution order every time you start writing Lua in a new project gets old fast.
I genuinely like Lua as a language - the same way I like Tcl, Scheme, and Io. They are all beautiful and powerful and perform very well in some scenarios. Elisp is ugly in comparison, but it's way more practical for medium-sized codebases. Being tied to Emacs is a considerable downside which limits its applicability, but focusing on language features alone, larger codebases are more practical to write in Elisp than in Lua. Plus, there's an escape hatch - Common Lisp or Clojure, pick your poison - for cases where Elisp actually doesn't cut it. There's no such easy way out for Lua.
I think there are some Lisp/Clojure inspired languages developed for Neovim which are used in Lua.
https://github.com/Olical/conjure
And on "it's not just an extensibility language": in my experience this doesn't matter. I get that "well the editor itself is half written in elisp" and so vaguely that is superior, but it is only so in an academic sense.
Expose the primitives for the editor in some API in _any_ langauge and you can basically achieve the same thing anyway, so pick a language that doesn't make me want to poke my eyeballs out with a hot skewer.
Sorry, rant over.
I believe it's more a question of how easy the redefinition is to implement. You can live-update a running Java or C programs, it's just less convenient/harder to pull off than with Forth, Smalltalk, Lisp, Prolog, and the like. So I think that yes, in principle, every language could have it - it's just that you'd need a huge pile of hacks for some and a few simple instructions for others to get it.
There's no argument there; you're right. That's why V and Nim, for example, put reloadable things in a separate compilation unit and handle some things (global state at least) specially upon reload (if I understand what they do correctly.)
My point was that you can get quite close (sometimes with a massive pile of hacks and/or developer inconvenience), not that you can get the full experience (as in Smalltalk or Lisp) everywhere. Especially since the reloading being convenient is a large part of the experience, I think.