Event notification without mutex

Use std::condition_variable_any you can use any class with it which implements the BasicLockable Concept.

Given a bad feeling about this I checked the implementation of std::condition_variable_any of libc++. It turns out that it uses a plain std::condition_variable together with a std::shared_ptr to a std::mutex, so there is definitely some overhead involved without digging any deeper. (There is some other post here on SO which covers this, though I first have to search that)
As a matter of that I would probably recommend to redesign your case so that synchronization is really only done by a mutex protecting a plain condition variable.

In some threading models (although I doubt in modern ones) the mutex is needed to protect the condition variable itself (not the object you're synchronizing) from concurrent access. If the condition variable wasn't protected by a mutex you could encounter problems on the condition itself.

See Why do pthreads’ condition variable functions require a mutex?

I have some object, which already internally synchronized - I don't need mutex to protect it. One thread should wait for some event associated with that object, and others would notify.

If you don't hold the mutex the waiting thread is going to miss notifications, regardless whether you use condition_variable or condition_variable_any with the internal mutex.

You need to associate at least one bit of extra information with the condition variable, and this bit should be protected by a mutex.