Re-land "[lldb] Synchronize output through the IOHandler"

Add synchronization to the IOHandler to prevent multiple threads from
writing concurrently to the output or error stream.

A scenario where this could happen is when a thread (the default event
thread for example) is using the debugger's asynchronous stream. We
would delegate this operation to the IOHandler which might be running on
another thread. Until this patch there was nothing to synchronize the
two at the IOHandler level.

Differential revision: https://reviews.llvm.org/D121500