ACR ON FINAL FOR LAX RWY 25L; CHANGED TO RWY 25R; EXPERIENCED NMAC AT 3500; WHEN EMER ACFT FOR RWY 25L OVERFLEW REPORTER'S ACFT.

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OUR FLT PLANNED RTE WAS THE TRANSITION FOR THE STAR. WE WERE CLRED TO DSND TO CROSS INTXN 1 AT FL180 AND 270 KIAS. APPROX 3 MI BEFORE INTXN 1; SOCAL APCH TOLD US TO DSND AND MAINTAIN 14000 FT. WE WERE NOT TOLD TO DSND VIA THE STAR; AND NONE OF THESE CLRNCS (SPDS/ALTS) WERE WHAT WE EXPECTED FROM THE STAR. APCHING RIIVR; WE WERE CLRED FOR THE ILS RWY 25L APCH AT 14000 FT. AT ABOUT 4000 FT; I ENGAGED THE APCH MODE OF THE AUTOPLT. SHORTLY AFTERWARD; LAX TWR CANCELED OUR APCH CLRNC AND ORDERED A DSCNT TO 2500 FT. NO LATERAL GUIDANCE WAS GIVEN SO I STAYED ON THE LOC FOR RWY 25L. NO MISSED APCH INSTRUCTIONS WERE GIVEN EITHER. WE THEN RECEIVED A TA ON OUR TCAS AND VISUALLY SAW A B757 COMING IN FROM OUR L; IN A L TURN; DSNDING; BELLY UP TO OUR ACFT. TWR THEN ASKED IF WE HAD THAT ACFT IN SIGHT TO WHICH WE REPLIED YES. TWR THEN SAID WE WERE CLRED FOR A VISUAL APCH TO RWY 25R AND THAT THE OTHER ACFT WAS A JET WITH A POSSIBLE ENG OVERHEAT (NO PRIOR WARNING HAD BEEN GIVEN TO US). AT THIS POINT I DISENGAGED THE AUTOPLT AND BEGAN MANEUVERING TO EXPEDITE OVER TO THE R RWY. IT WAS HARDLY A POS TO EXECUTE A SIDESTEP MANEUVER BECAUSE I WAS VISUALLY AVOIDING A COLLISION WITH THE OTHER JET. I TOLD MY FO TO SET UP FOR THE ILS TO THE R RWY -- WHICH WE DID RIGHT AWAY. SINCE THE GS ON RWY 25R WAS NOTAM'ED INOP; WE BEGAN TO SET UP FOR AN LNAV/VNAV TO BACK UP OUR VISUAL WHILE WE PROCEEDED TO INTERCEPT THE LOC RWY 25R. AT THIS POINT; TWR ASKED AGAIN IF WE SAW THE B757. I LOOKED TO MY L AND THEN BACK OVER MY L SHOULDER AND STILL COULD NOT SEE THE ACFT. WE TOLD TWR THAT IT WAS NO LONGER IN SIGHT. MY FO RAN HIS MAP DISPLAY TO THE MINIMUM SCALE AND NOTED THAT THE ACFT WAS ON TCAS RIGHT BEHIND US. IT WAS PROBABLY WITHIN A WINGSPAN. THE TCAS NOTED THE ACFT HAD +100 FT OF SEPARATION. HE WAS DSNDING ON TOP OF US FROM ABOVE. WE WERE ON RWY 25R CTRLINE AT ABOUT 3 MI AND 1000 FT ABOVE THE RWY WHEN WE STARTED TO OBSERVE SEPARATION. BOTH ACFT LANDED SIMULTANEOUSLY ON THE PARALLEL RWYS. THE B757 WAS CLRED FOR THE VISUAL TO A RWY TO WHICH WE HAD ALREADY BEEN CLRED. THE CTLR'S DIRECTION TO US WAS JUST TO DSND INSTEAD OF LEVELING OFF AND DIRECTING A MISSED APCH OR SOME APPROPRIATE. THEN; THE CTLR ASKED IF WE SAW THE B757 THAT WAS IN THE MIDDLE OF OUR WINDSCREEN; AND; WHEN WE SAID YES; HE DECIDED HE HAD ENOUGH INFO TO GRANT US A NEW CLRNC FOR A VISUAL APCH TO THE ADJACENT RWY. AT THAT POINT; HE CEASED CTLING BOTH ACFT. THE OTHER JET MAY HAVE BEEN DEALING WITH A SELF INDUCED EMER BY TRYING TO RUSH A LNDG FOR WHICH THEY HAD NOT BEEN SET UP PROPERLY. THIS WAS EVIDENCED BY THE FACT THAT THE ACFT OVERSHOT THE CTRLINE AND INTRUDED IN THE APCH COURSE FOR THE PARALLEL RWY. UNFORTUNATELY; THAT ACFT NEARLY LANDED ON TOP OF OURS.