Unless Rust has gotten runtime reflection without me hearing about it, I don't think writing the compiler in Rust gives you any special powers in interfacing with Rust. You'd get a lot more of a win from parsing the DWARF of a library when you dlopen() it, and using the type information that exposes to be able to use the full Rust ABI rather than the C ABI.
EDIT: Actually, no, even with runtime reflection, that would only help an interpreter, not a compiler.
That still wouldn't give you the ability to perform template instantiations at runtime though -- for that, you'd need to ship the Rust compiler with your Lisp _applications_, since you might be able to invoke a Rust template with arguments at runtime that hadn't been seen before.
If you're looking at work on building a more modern Lisp compiler, check out SICL or Clasp, though as far as I'm aware, those are both early-ish projects.