[lldb][dap] Avoid concurrent `HandleCommand` calls (#83162)

The `EventThreadFunction` can end up calling `HandleCommand`
concurrently with the main request processing thread. The underlying API
does not appear to be thread safe, so add a narrowly scoped mutex lock
to prevent calling it in this place from more than one thread.

Fixes #81686. Prior to this, TestDAP_launch.py is 4% flaky. After, it
passes in 1000 runs.