What was found
(CAN) DURING THE TAKE OFF ROLL, THE SMOKE AFT LAV WARNING MESSAGE BECAME EVIDENT. THE LAVATORY SMOKE ALARM WAS GOING OFF AND THERE WAS A PRESENCE OF SOME SMOKE ACCORDING TO THE FLIGHT ATTENDANT. MAINTENANCE PERFORMED SOME TROUBLESHOOTING AND IN COMBINATION WITH THE HISTORICAL ASSOCIATION OF THIS ANOMALY WITH A MALFUNCTION IN THE APU ELECTED TO PLACE THE APU ON MEL. THE AIRCRAFT RETURNED TO SERVICE. LATER THE APU WAS REPLACED AND THE MEL WAS REMOVED.