Locks, systems and methods of monitoring a lock, the lock having a hub with a slot rotatable by a handle to open and close a latchbolt. A locking member is moveable into and out of engagement with the hub slot to prevent and permit movement of the hub and latchbolt. A sensor on the lock, adjacent the hub and locking member, monitors a moving lock component. The sensor may sense the position of the locking member in or out of engagement with the hub slot. The sensor may be a reed switch actuated by a magnet on the moving lock component. The lock may further include a magnet mounted on the hub and the sensor may comprise a reed switch capable of being actuated by the magnet on the hub. The lock and system may include an external control unit having an alarm for controlling operation of the lock.