> It keeps track of PID of the last process that acquired it, and if another process can’t acquire it, it can check if the PID is still alive using stat, if it’s dead it will unlock the mutex and reset the field of previous owner.

That's not safe. PIDs are recycled.

The only correct solution I can think of is to place the lock in shared memory, use the futex(2) API, and use set_robust_list (https://linux.die.net/man/2/set_robust_list) to ensure the kernel will unlock a futex if a process dies.

You may (should?) be able to initialize a pthread-based PTHREAD_PROCESS_SHARED + PTHREAD_MUTEX_ROBUST mutex in a shared memory region and have everything just work.