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"Rust-like LISP"

The phrase was ambiguous. I meant a LISP w/ safe, memory model like Carp. There's already LISP's in the past and present for OS's. There's also projects that restrict the power of languages to get better efficiency in low-level work. So, more of the latter with Rust's memory model might be advantageous. The former with their flexibility could be built on top of that same language with a low-latency GC for anything done dynamically or which the analyzer just couldn't handle enough to know safety. Might lead to a great performance boost on top of safety benefits.

"Safe software can also be written in other languages than Rust. Ada is still industry standard of safe programming today."

You're right that Ada was a language systematically designed for safety that people could be using right now. I gave them some resources on that here:

https://news.ycombinator.com/item?id=15771552

The problem: Ada does not have temporal safety or flexible support for race-free concurrency. The first part in Ada doesn't exist at all: they have to do unsafe deallocation when their tricks like memory pools aren't enough. The second, Ravenscar, is like a tome in its restrictions compared to the basic rules of the borrow-checker in Rust. Rust smashes Ada so hard on "safety without GC concept" that I told Yannick McCoy at AdaCore to get someone on achieving parity pronto. For SPARK if nothing else since it would have provably-safe sequential procedures whose composition was also safe w/ Rust's method. That would be awesome for projects such as IRONSIDES DNS.

"Rust shines in the field where Mozilla developed it for -- safe Internet browsers."

Rust shines anywhere you want safe, systems code without a GC and with concurrency. That's it's main selling point, not language design. There's tons of applications for that as the huge ecosystem is showing us replacing all sorts of components in other languages with safe, fast alternatives. Redox OS did an OS in it. In high-assurance sector, Robigalia was wrapping seL4 so one can have safe apps in Rust on a formally-verified, separation kernel. bluejekyll upthread wrote a DNS server (TrustDNS) in it. Rust can do about anything an analyzable subset of C can do.

"The Lisp version would just not be as performant as Ada's and Rust's."

This is correct. My recommendation to use one close to the metal like PreScheme with Rust-style safety that outputs C for LLVM attempts to address that. All the macros apply until the resulting code is straight-forward. The translation should be straight-forward to C where LLVM does the heavy lifting. One might also use techniques from projects such as Chicken Scheme, a whole-program optimizer, and/or a super-optimizer. The speed differences might be so minimal that nobody even cares. They already are for several LISP's on most applications but I'm talking system code.