For the LSP, you can have a look at the install instructions of some packages, e.g. Installation – Larecs🌲
For the run configuration I do not have a nice solution. For run, I often use the internal console. For debug I defined a build task that executes mojo build and set this as a prerequisite of the run. This works somewhat well, though it clutters the workspace with the built executables.
I am currently afk but could post my scripts tomorrow. Would be curious to see if others have better solutions. I really think this would be a great native feature to have for the vscode extension.