I've been hanging out a good amount in the #bootstrappable IRC channel on Freenode lately. They seem to have a decent start at a fresh new stack that builds all the way up from machine code and can run a decent amount of C (as of last night: gcc, binutils, libc). There's also parallel infrastructure to build tiny proof-of-concept Lisp and Forth interpreters.
There's a decent amount of documentation, but I'm still finding my way around it. Not clear what order to read things, etc. The good news is that it builds. On any Linux system, 32-bit or 64-bit, you should be able to just run `make`. There's not a lot of code, and it seems worth spending time to understand. The folks on the IRC channel have been super helpful to answer questions.
This doesn't answer your immediate question. But I'm hopeful that we can build a new Lisp something like this that will be approachable and hackable, and good for sharing code and runtime across language boundaries. Which would reduce the gap between Lisp and systems programming, or any other domain.
I have this constant problem of dissatisfaction with existing tools and paradigms, to the point that I often work my way down to the bottom of the stack considering building a new OS...
My most recent descent has started with a dissatisfaction of container orchestration tools, then discovering that it's not really easy to manage containers with unprivileged code under Linux, and now wondering about building a microkernel OS / language for distributed actor-model development from the ground up, and thinking it would be nice to have an "OS development framework" so it is easier to experiment with novel architectures without having to deal with a lot of driver development grunt work... I originally asked this question somewhere near the beginning of all that.
Speaking of building a new OS, check out https://gitlab.com/giomasce/asmc which uses some of the bootstrappable infrastructure to build an OS. It uses a stack-based (Forth-like) intermediate language called G to implement C.