Is it possible to use the notify method on an Object without owning the synchronized lock?

No, the notify() method of the Object object cannot be called without owning the monitor (lock) of that object, that is, without using synchronized. If notify() is called outside a synchronized block, an IllegalMonitorStateException will be thrown.

Example of correct usage:

synchronized(obj) {
    obj.notify();
}

This is because notify() notifies one of the threads waiting on the object's monitor, and proper operation requires owning that monitor.