What was found
WHILE ENROUTE AT CRUISE, THE DOOR 2L LAV SMOKE DETECTOR ACTIVATED AND A THIN LAYER OF SMOKE DEVELOPED IN THE CABIN. SMOKE LATER DISSIPATED. CREW COMPLETED THE QRH FOR SMOKE, FIRE OR FUMES. CREW ELECTED TO DIVERT. EMERGENCY DECLARED AND DISPATCH AND MC WERE NOTIFIED. OXYGEN MASKS WERE NOT REQUIRED, NO SMOKE OF FUMES EVIDENT IN COCKPIT. MAINTENANCE PERFORMED A HIGH POWER ENGINE RUN AND DETERMINED THE NR 1 ENGINE TO BE SOURCE OF THE SMOKE. ENGINE WAS REPLACED.