It would be a lot easier than inventing Rust, for two reasons:
1. You don't need to write a parser.
2. The target language for your DSL compiler can be Common Lisp rather than machine language without sacrificing performance.
Those two things make it absolutely certain that however much work it is to re-invent Rust in CL it will be strictly less work than inventing Rust from scratch.
There are other benefits to this approach as well. For example: if, after implementing your DSL you discover that you've made a sub-optimal design decision somewhere along the line, it will be a lot easier to tweak your DSL than it is to tweak Rust.