B757-200 CREW RECEIVES TCAS RA JUST OUTSIDE JETSA ON THE ILS 24R AT LAX AND GOES AROUND FOLLOWING TCAS GUIDANCE.

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WE WERE LEVEL AT 2200 FT MSL OUTSIDE OF JETSA WHEN WE GOT A 'TFC; TFC' AUDIO/YELLOW POP-UP ON THE HSI. WE THEN GOT A RED RA/AUDIO 'CLB; CLB' WARNING. MY EXCELLENT FO BEGAN TO FOLLOW THE RA GUIDANCE BARS AND I SAW THAT THE RA ALT WAS 1900 FT MSL AND WE WERE 2000 FT MSL. MY FO CLBED FASTER AND THE RA SYMBOL STAYED WITH US AT 100 FT BELOW OUR ALT. I TOLD LAX TWR THAT WE HAD AN RA ALERT AND WE WERE CLBING/GOING AROUND. LAX TWR TOLD US TO CLB TO 3000 FT AND TO FOLLOW THE LOC. I ASKED IF WE COULD FLY RWY HDG INSTEAD. HE SAID OK. THE RA DISAPPEARED AT 2900 FT MSL. I DO NOT REMEMBER HEARING THE TCAS CLR OF CONFLICT AUDIO ANNOUNCEMENT. AT THIS POINT WE GOT THE LOW FUEL EICAS MESSAGE ALONG WITH THE MASTER CAUTION LIGHTS AND THE BEEPER. I GOT OUT THE HANDBOOK AND FOLLOWED THE SOP BY OPENING THE XFEED VALVE AND TURNING ON THE CTR FUEL PUMPS. WE TURNED DOWNWIND NORTH AND TOLD SOCAL THAT WE HAD LOW FUEL AND 5500 LBS OF FUEL REMAINING. WE TURNED BASE 3 MI E OF JETSA AND HAD NO FURTHER INCIDENT. WE LANDED WITH 5100 LBS OF FUEL. ON THE GND OUR CTLR TOLD US THAT THERE WAS NO TFC IN OUR IMMEDIATE AREA AND THAT A HELI WAS 3 MI BEHIND US AND OFFSET AT LOW ALT. WE BELIEVE THAT THE WARNING WAS A FALSE INDICATION. HOWEVER; WE FOLLOWED SOP. HUMAN FACTORS AT HAND WERE: WE WERE VERY TIRED AS OUR FLT THE NIGHT PRIOR WAS LATE AND TURNED INTO A LATE NIGHT FLT WHICH ARRIVED IN THE EARLY MORNING. OUR FLT OUTBOUND WAS DELAYED DUE TO UNKNOWN REASONS AND WE ARRIVED INTO LAX AT XA55 WHICH WAS EXACTLY 2 HRS LATE. THE RA WARNING OCCURRED AT A CRITICAL TIME; RIGHT AT GS INTERCEPT AND THINGS GOT VERY BUSY. SINCE WE WERE CLBING QUICKLY WE NEVER REALLY ACCELERATED MUCH ABOVE THE BUG. WE PERFORMED A GAR TO CLEAN CONFIGN AND RETURNED TO LAND ON RWY 24R. ATC SAID THAT NO FURTHER INFO WAS REQUIRED AND TO HAVE A GOOD NIGHT. I CALLED DISPATCH AND ADVISED OF THE SITUATION. MY FO WROTE UP THE TCAS AND CALLED MAINT.