B757 LINES UP WITH WRONG RWY IN LAX AIRSPACE.

Narrative

APCH CTL CLRED US FOR A R DOWNWIND VISUAL TO RWY 24R AFTER COPLT; WHO WAS FLYING; STATED THAT HE HAD RWY 24R IN SIGHT. BEFORE TURNING BASE; APCH CTL ASKED IF WE COULD SEE B737 TFC AT OUR 1 - 2 O'CLOCK POS. WE RESPONDED 'NEGATIVE.' I WAS TRYING TO IDENT THE LOC AT THE TIME. AS WE TURNED BASE; I WAS GETTING PARTIAL LOC IDENTS. APCH CTLR THEN TURNED US TO A HDG OF 220 DEGS TO INTERCEPT RWY CTRLINE AND SWITCHED US OVER TO TWR. ABOUT THAT TIME WE SAW A B737 ON FINAL SLIGHTLY AHEAD; TO OUR L; AND BELOW US. WE QUERIED TWR ABOUT THE B737'S LNDG RWY AND WAS TOLD IT WAS LNDG ON RWY 25R AND THAT WE HAD GONE THROUGH THE RWY 24R CTRLINE. WE REALIZED OUR MISTAKE AND TURNED BACK TOWARD RWY 24R AND LANDED UNEVENTFULLY. BELIEVE PROB WOULD HAVE BEEN AVOIDED IF WE HAD GOTTEN POSITIVE LOC IDENTS AND SWITCHED EFIS TO ILS EXPANDED MODE. BOTH HEADS SHOULD HAVE BEEN OUTSIDE THE COCKPIT. CONTRIBUTING FACTOR WAS COPLT SAYING HE HAD RWY 24R IN SIGHT BEFORE BEING CLRED FOR THE VISUAL. COPLT HAD FLOWN OUT OF LAX FOR SEVERAL YRS AND WAS QUITE FAMILIAR WITH THE LAYOUT.