DURING ARRIVAL, A BOEING 747, REGISTRATION NUMBER D-ABYP, LUFTHANSA FLIGHT 5432, WAS VECTORED FOR AN ILS LOCALIZER BACKCOURSE APCH TO RWY 19 AT THE NEW ORLEAN INTL ARPT. WHILE ON THE APCH AT 2000 FT MSL, THE AIRCREW WERE INSTRUCTED BY THE ARRIVAL CONTROLLER TO CONTACT THE TOWER ON ANOTHER FREQUENCY. SHORTLY AFTER THAT, THE ARRIVAL CONTROLLER OBSERVEDA VFR CODED TARGET APPEAR ON THE RADAR. HE ATTEMPTED TO ADVISE THE BOEING CREW BY USING AN OVERRIDE FEATURE, BUT AT THAT TIME, ANOTHER CONTROLLER WAS TRANSMITTING. THE BOEING CREW SAW THE ACFT COMING HEAD-ON & TOOK EVASIVE ACTION BY MAKING A STEEP TURN TO THE RIGHT. THE OTHER ACFT WAS A LIGHT SINGLE ENG PLANE THAT WAS FLYING AT 2000 FT MSL. THE LIGHT PLANE WAS NEVER IDENTIFIED & WAS NOT OBSERVED TO TAKE EVASIVE ACTION. A GROUP II TERMINAL CONTROL AREA (TCA) WAS IN PLACE AT NEW ORLEANS. THE NEAR COLLISION OCCURRED WHERE THE MIN ALT FOR THAT PART OF THE INSTR APCH WAS AT THE BOTTOMOF THE TCA. VFR FLT UP TO THE BOTTOM OF THE TCA IN THAT AREA WAS LEGAL. THE NUMBER OF OCCUPANTS IN THE SE ACFT WAS UNKN.