FLT ATTENDANT RPTED SMOKE ALARM AND BURNING ODOR COMING FROM AFT LAVATORY WITH NO VISIBLE INDICATION OF FIRE IN LAVATORY. FLC LANDED AFTER DECLARING AN EMER. A SECOND TKOF WAS MADE FOLLOWED BY ANOTHER FLT ATTENDANT RPT OF SMOKE AND ODOR. THE SECOND EMER WAS DECLARED AND THE LNDG MADE WITHOUT INCIDENT.

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ON CLBOUT AFTER TKOF FROM RWY 22R JFK; FLT ATTENDANT RPTED R AFT LAVATORY SMOKE ALARM GOING OFF; AND A BURNING ODOR. COCKPIT CREW DONNED MASKS; DECLARED EMER AND ASKED FOR A RETURN TO JFK. WE CALLED OUT FIRE TRUCKS; AND PREPARED FOR A VISUAL LNDG RWY 31R AT JFK. SMOKE ALARM CONTINUED TO SOUND UNTIL SHORT FINAL. WE MADE AN UNEVENTFUL LNDG AT JFK. WE CHKED CABIN FOR SMOKE OR FIRE; FOUND NEITHER; AND TAXIED TO GATE FOR MAINT. CREW COORD WAS OUTSTANDING. FO FUNCTIONED WELL AS GO BTWN WITH CABIN CREW. CABIN CREW HANDLED THE SIT VERY PROFESSIONALLY. THEY SEPARATED DUTIES; COMMUNICATED WELL AND GAVE THE COCKPIT CREW TIME TO FOCUS ON THE EMER LNDG. GREAT CRM! SUPPLEMENTAL INFO FROM ACN 433459: FLT ATTENDANT NOTIFIED US THE AFT LAVATORY SMOKE DETECTOR WAS GOING OFF AND THAT SHE SMELLED A SLIGHT ODOR OF SMOKE. SHE CHKED LAVATORY AND WASTE BASKET FOR FIRE AND SMOKE; NONE WAS NOTED. WE DONNED OXYGEN MASK AND DECLARED AN EMER. RAN CHKLIST AND KEPT IN CONTACT WITH FLT ATTENDANT DURING THE ENTIRE SIT. SUPPLEMENTAL INFO FROM ACN 433128: TOOK ACFT THAT WE HAD PREVIOUSLY TAKEN OFF WITH. PROB WAS SIGNED OFF AS EXCESS OIL IN APU SUMP AREA; SEEPING INTO DUCT WORK. AFTER SIGNOFF; WE TOOK ACFT AND HAD SAME AFT LAVATORY SMOKE ALARM GO OFF AT 3000 FT. FLT ATTENDANTS CALLED AND RPTED SAME. DECLARED EMER AND PERFORMED A SECOND EMER LNDG. CANCELED FLT. SUPPLEMENTAL INFO FROM ACN 433127: FLC DONNED OXYGEN MASKS AND DECLARED EMER. EMER EQUIP WAS CALLED OUT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE FO SAID THAT MAINT CLRED THE ACFT FOR FLT AFTER THE FIRST INCIDENT AND AFTER THE SECOND INCIDENT THE ACFT WAS REMOVED FROM SVC. IT WAS HIS IMPRESSION THAT THE APU WAS TO BE REMOVED FROM THE ACFT AND REPAIRED.