What I do is select the “Import project root : /path/to/cwd/” option proposed by M-x lsp. It seems to somehow remember from then (never asks again for the directory)
I’m not sure exactly what this does. I suspect only one server is launched for a “project”. And the directory set here is meant to be the root of the current “project”, i.e. all buffers/files open in the this directory will share the same lsp server.