A PASSENGER HAD DISCARDED A CIGARETTE BEFORE LEAVING THE LAVATORY. THE FLIGHT ATTENDANT FOUND SMOKE ISSUING FROM THE WASTE BIN AND EXTINGUISHED THE FIRE. THERE WAS NO INDICATION IN THE COCKPIT OF SMOKE OR FIRE. A LATER CHECK OF THE SMOKE DETECTOR SHOWED IT DID NOT ACTIVATE WHEN SMOKE WAS GENERATED IN THE LAVATORY. THE OPERATOR ADHERED TO THE AIRCRAFT MANUFACTURER'S RECOMMENDED MAINTENANCE PROGRAM; THE PROGRAM CONTAINED NO PROCEDURE OR INTERVAL FOR CLEANING SMOKE DETECTORS OR DUCTING. THERE WAS NO OPERATIONAL TEST WHICH DEMOSTRATED A DETECTOR COULD SENSE SMOKE.