Certainly such systems can pretty readily exist. You merely need atomic reads/writes in order to implement locks.
You can't create userspace locks which is a bummer, but the OS has the capability of enforcing locks. That's basically how early locking worked.
The main thing needed to make a correct lock is interrupt protection. Something every OS has.
To go fast, you need atomic operations. It especially becomes important if you are dealing with multiple cores. However, for a single core system atomics aren't needed for the OS to create locks.
You can't create userspace locks which is a bummer, but the OS has the capability of enforcing locks. That's basically how early locking worked.
The main thing needed to make a correct lock is interrupt protection. Something every OS has.
To go fast, you need atomic operations. It especially becomes important if you are dealing with multiple cores. However, for a single core system atomics aren't needed for the OS to create locks.