What was found
(CAN) SHORTLY AFTER TAKEOFF, THE LAVATORY SMOKE DETECTOR SOUNDED, EMERGENCY DECLARED. AIRCRAFT RETURNED AND OVERWEIGHT LANDING CARRIED OUT. HEAVY LANDING CHECK CARRIED OUT, ALL OK. REPLACED SMOKE DETECTOR. GROUND RUN SERVICEABLE. NEXT FLIGHT, SMOKE DETECTOR SOUNDED. AUXILIARY POWER UNIT AT FAULT. AIRCRAFT OPERATED UNDER MEL. APU TO BE REPLACED.