What was found
(CAN) DURING THE CRUISE PORTION OF THE FLIGHT THE FLIGHT ATTENDANT INFORMED PILOT OF A BURNING SMELL IN THE AFT LAVATORY. SOON AFTER THEY INFORMED THE PILOT THAT THERE WAS SMOKE COMING FROM THE CEILING. A DIVERSION WAS INITIATED TO THE NEAREST AIRPORT (YQT). SMOKE AND FUMES QUICK REFERENCE CHECKLIST (QRC) WAS COMPLETED AND THE SMOKE DISSIPATED. YQT MAINTENANCE REPORTED THAT THE SOURCE OF THE SMOKE WAS A BURNT AFT LAVATORY LED TASK LIGHT UNDER THE MIRROR. THE SPARE SOAP CONTAINER LEAKED IN THE STORAGE COMPARTMENT CAUSING THE LIGHT TO SHORT OUT. ALL 3 LAVATORIES WERE INSPECTED AND FOUND EACH COMPARTMENT CONTAMINATED WITH SOAP. SPILLED SOAP WAS CLEANED AND POWER WAS REMOVED FROM TASK LIGHT SYSTEM IN LAVATORY. SYSTEM PLACED ON MEL.