A B737-300 FLT ATTENDANT RPTED SMOKE IN THE AFT LAV APPARENTLY CAUSED BY A LAV FLUORESCENT LIGHT BALLAST. THE CABIN CREW REPORTED THAT THE SMOKE DETECTORS DID NOT ACTIVATE. THE FLT CREW DECLARED AN EMER AND DIVERTED WHILE THE FLT ATTENDANTS EXTINGUISHED THE FIRE.

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DURING CRUISE FLT; 60 NM NE OF ZZZ; THE 'C' POSITION FLT ATTENDANT NOTIFIED THE FO VIA INTERPHONE IN AN EXCITED MANNER THAT THERE WAS SMOKE BILLOWING FROM ACFT L; AFT LAV. SHE STATED THAT THE 'B' FLT ATTENDANT WAS FIGHTING THE APPARENT FIRE WITH HALON AND WATER FIRE EXTINGUISHERS. FLT CREW REQUESTED AN IMMEDIATE DSCNT AND CLRNC FOR DIRECT ZZZ AND DECLARED AN EMER. AN EXPEDITIOUS DSCNT AND UNEVENTFUL LNDG WAS ACCOMPLISHED. THE FIRE EXTINGUISHED PRIOR TO LNDG. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR WAS INFORMED UPON INQUIRING WITH ACR MAINT THAT THE AFT LAV FLUORESCENT LIGHT BALLAST OVER THE SINK FAILED AND WAS EMITTING A GREAT DEAL OF SMOKE. THERE WAS NO PERIPHERAL DAMAGE TO THE FIBERGLAS SIDE WALL. IT IS OF CONCERN TO THE RPTR THAT THE ASSOCIATED LAV MIRROR CB DID NOT POP SO THE CREW COULD NOT HELP WITH ISOLATING THE PROB INFLT. NO PAX WERE AWARE OF THE PROB UNTIL THE CREW ANNOUNCED A DIVERSION. THE FLT CREW HAD THE ACFT ON THE GND APPROX 6 MINUTES AFTER BEING NOTIFIED. SUPPLEMENTAL INFO FROM ACN 677365: SMOKE ALARM DID NOT GO OFF.