Hello, and of course, you're welcome.
Sorry, I missed the first part of the question and only answered the second part about the LSP implementation. I don't know of any known issues with SourceKit on Windows (though that doesn't mean that there aren't any), and the CI should be building and testing it as well. I don't know about executables for SourceKit, but the library for SouceKit should be part of the build (sourcekitdInProc.dll). As you mentioned - sourcekitd-test works and that is used as part of the test suite. Personal wishful thinking on my part - I would like to see an out-of-proc SourceKit server using COM on Windows, but that doesn't seem like a blocker to the use of SourceKit currently.
The LSP implementation would be the more interesting aspect I think because it should stress test the implementation and help flush out issues that may have been missed.