I don't know if this is a stupid question, but could one design a very basic LISP machine on a FPGA? how about a diminutive JVM?

Why not? It was done on real hardware in the 80s, right? hell, here's one:

http://www.aviduratas.de/lisp/lispmfpga/

It's very easy. Personally, I find Reduceron [0,1] far more interesting.

[0] https://www.cs.york.ac.uk/fp/reduceron/

[1] https://github.com/reduceron/Reduceron

I made a little FPGA LISP machine:

https://github.com/jbush001/LispMicrocontroller

A few ARM CPUs have not a JVM, but the ability to accelerate a JVM by directly executing Java bytecode (Jazelle DBX).

"The Jazelle extension uses low-level binary translation, implemented as an extra stage between the fetch and decode stages in the processor instruction pipeline. Recognised bytecodes are converted into a string of one or more native ARM instructions."

Cool, haven't thought about that. I probably need to get an FPGA. Really liked the book "The Elements of Computing Systems" [1][2] in which one builds a computer from NAND gates upwards, a compiler, vm and finally a simple OS with applications. The hardware part of the course seems to be on coursera now as well. [3]

[1] https://mitpress.mit.edu/books/elements-computing-systems

[2] http://www.nand2tetris.org/

[3] https://www.coursera.org/learn/build-a-computer

That's some really neat stuff that I somehow missed in prior research. Thanks for the links. I'm particularly going to have to take another look at the paper that details their methodology for building systems ground up. The abstraction process and samples.