You just have to think a bit differently about your synchronization primitves. You don't have locks, you have a message queue and that is your synchronization primitive. A resource that should only be accessed by one thread is abstracted away using an actor, and the queue guarantees that only one process at the time has access, as the actor can only process one message at a time.

You can implement locks using actors if you really want to. An actor represents the state of the lock and stores which actor locked it and only responds to the unlock message from that actor and ignores all lock and unlock messages from all the other actors until it is unlocked.