We have Guix as a system configuration/package manager, the GNU Shepherd as an init, and the GuixSD initrd itself, all of which are written in Guile Scheme.
With the GNU Hurd important parts of the OS could be written in Scheme as well.
The problems start with the desktop, where we don't really have anything that's well-integrated and lispy. Sure, there's StumpWM (Common Lisp), and there's Emacs, but they are separate programmes and there's no link between them.
There is McCLIM[1], a GUI toolkit which looks like a continuation of lisp machine ideas, but as far as I know it does not have an active community (unlike Guix and Guile, whose communities actively work on a Scheme-powered operating system).
I really wish the GNU project would standardise on Common Lisp rather than Scheme. Lisp-2, false NIL, full-powered macros — Common Lisp has a lot going for it.
An emacs written in Common Lisp, running in StumpWM, running atop a CL Guix, Shepherd & GuixSD would be a thing of beauty.
The thing that tends to push me into agreement is that common lisp is compiled whereas scheme/guile is bytecode. If we want to use lisp for OS purposes I think it needs to be compiled for the speed benefits. Is there any other lisp or similar language that is compiled?
Maybe I just irrationally don't trust bytecode vm's.