Yes, I was thinking about someone going many step furthers, like Elixir is for Erlang and the BEAM, someone who disagrees with design decisions of the Julia language but appreciates the compiler's capabilities and the ecosystem enough to use them to implement their own vision for a programming language. Making it a Lisp is just one of the more obvious scenarios, as someone may like Julia in general but want the full power of s-expressions.

How is Elixir’s design different from Erlang’s? Semantically they’re pretty much the same language.

A better example would be Java/Clojure.

Elixir is basically Erlang, just like Lisp Flavored Erlang and Gleam (the statically-checked language for the BEAM). The BEAM in general is a very specialized VM, which is why I used as an example, as the Julia compiler is also a very specialized platform and other languages targeting it would also be just Julia. Like Julia with s-expression, a typescript like extension for Julia that maybe would focus on different tradeoffs by reducing polymorphism in exchange for type checked contracts (but still use the same machinery and ecosystem since it would compile to Julia/Julia IR). I really wouldn't expect something completely different like the JVM supports (as at this point it would be better to use the LLVM directly).