That's an amazing idea, I take it you've read the other MIT memos already?
http://wiki.xxiivv.com/docs/memo444.html

The CADR emulator is well maintained and somewhat stable now as of 101v, you should poke at it see how the VM handles the bytecode.

For an interesting different processor, it's not lisp but just for the IO alone, the T4 Transputer is really interesting, and might give you some ideas for lisp machines if you're interested in parallelism

Right! Well, you're in for a treat because lisp machines are fantastic, weather academia is interested or not.. that's a different story.

Have you had a look at LISPkit and SECD machines? It's not quite lisp machines, but good related material that gave me a sort of "AH!ha!" moment, they're well documented but don't worry if implementing it is too daunting.. it's.. a lot.
https://git.sr.ht/~rabbits/lispkit
also: https://github.com/Interlisp/maiko

GitHub - Interlisp/maiko: Medley Interlisp virtual machine

Medley Interlisp virtual machine. Contribute to Interlisp/maiko development by creating an account on GitHub.

^GitHub

Good luck 😀 If you get stuck with lispkit, let me know. Try the CADR emulator if you can, the folks on the mailing list are super responsive, I think one of them is on the fedi too.

Here's a few related memos that might be good to read too:
http://wiki.xxiivv.com/docs/memo1564.html
http://wiki.xxiivv.com/docs/memo528_cadr.html

also:
http://wiki.xxiivv.com/docs/baker_thermodynamics.html

Here's a nice transputer emulator that works well, try running MINIX on it from the example if you've got a free evening sometimes.
https://github.com/pahihu/t4

GitHub - pahihu/t4: Highfield's Inmos T414 transputer emulator to run the Inmos Occam 2 Toolset.

Highfield's Inmos T414 transputer emulator to run the Inmos Occam 2 Toolset. - GitHub - pahihu/t4: Highfield's Inmos T414 transputer emulator to run the Inmos Occam 2 Toolset.

^GitHub

@neauoire

Have you checked Gyula Magó's 'string-reduction machine'? It was referenced in Kent Dybvig's dissertation as one of 3 compilatiin targets of Scheme, and it uses John Backus' applicative language FFP from his famous Turing-award lecture 'Can programming be liberated...' as its machine code