What was found
RDU TO CLE - AFTER TAKEOFF AT 1,500FT, THE CREW RECEIVED A LAV SMOKE EICAS MESSAGE. THE CREW PERFORMED THE CHECKLIST ITEMS FOR LAVATORY SMOKE AND PREPARED FOR A RETURN TO FIELD. THE FLIGHT ATTENDANT CONFIRMED THAT THERE WAS NO VISIBLE SMOKE NOR ODOR OF SMOKE. THE LAVATORY SMOKE INDICATION WENT AWAY ON FINAL APPROACH AND THE AIRCRAFT LANDED WITHOUT INCIDENT. MAINTENANCE INSPECTED THE AIRCRAFT AND FOUND NO SIGNS OF FIRE, BUT DID FIND THAT THE LAVATORY SMOKE DETECTOR WAS DIRTY. THE LAVATORY SMOKE DETECTOR WAS CLEANED AND THE ENGINES WERE RUN UP TO HIGH POWER WITH NO FURTHER INDICATIONS.