Despite the fact that asyncio.get_running_loop() never returns None but raises RuntimeError (and maybe other tiny cleanups), 
I can live with the proposal.

It doesn't make a system worse at least and backward compatible.
We can return to the idea of raising a warning from the constructor later, on collecting more feedback.

P.S.
There is a subtle non-deterministic behavior in the proposal: if the lock is accessed from a concurrent thread, the exception about wrong usage will be raised later at an arbitrary code point.
This is a well-known problem of the lazy initialization pattern and maybe we should do nothing with it. The programming is a compromise always.