Does Aristotle produce TLA+ output?

For example can it read rust async code and prove that there are no deadlocks in TLA+, or some equivalent in Lean?

TLA+ is generally used to specify a "toy model" of some complex distributed system. It's not intended for end-to-end proof, for that you'd just use Coq/Rocq or Lean itself. Lean is certainly expressive enough, but you'll have to translate the time and non-determinism modalities of TLA+ as part of the Lean development.