I don't have any code to show for it, but I spent some time looking at this and wanted to leave some info here in case it's useful to someone who's better at Rust than I am.

It seems to me that the important changes here would live in the code for the LSP Registry (currently in helix-lsp/src/lib.rs) and in Transport.recv() (currently in helix-lsp/src/transport.rs). The status of a Client can be queried by checking if client._process.id() is a None, in which case the client is dead and should be restarted. But this check would probably have to be triggered by an Error::StreamClosed caught asynchronously in Transport.recv(), which means an async block which currently isn't aware of the registry needs to mutate the registry (or be changed so that it can propagate the error to somewhere more suitable). I don't know enough async stuff do do this yet, but hopefully this comment can save some time for someone who does.