Apologies for the delayed response Dilipan, if it is an Optimistic locking then the second user should able to open it if he has the access. If it is Default locking mechanism then the second user can't open it.
If the lock expires, other users should be able to perform on the work object. I even confirmed the same at my end.
The assignment will not get greyed out for me even though the lock is held by some other operator(provided the first operator has access). If the assignment is greyed out, it means that the user doesn't have access to work on it.