Lockable itself isn't distributed (or, at the very least, doesn't appear distributed from the outside), so I'm not sure if linearizability applies here, but maybe I'm misunderstanding you comment.

In a similar vein, I guess you can ask what happens if a client first checks if a lock is available then tries to acquire it, in two separate steps; but in that case, there's no guarantee that the lock wasn't acquired in between checking and acquisition.

basically if it does not use synchronous replication. and master server switch then 2 client could think they own an unexpired lock.

But if it does synchronous replication without using a consensus algorithm like Paxos or Raft then the system become unwrittable if an instance go down.