AN ACR B737 FLC OVERSHOT THEIR TURN TO FINAL APCH ON RWY 24R AT LAX WHEN THE FO; WHILE ATTEMPTING TO CONFIRM THAT HE HAD THE TFC IN SIGHT; LOST THE RWY THAT HE WAS ASSIGNED AND INSTEAD FOCUSED ON A RWY TO THE S. THE CAPT REALIZED THE ERROR AS THEY OVERSHOT AND CORRECTED THEIR COURSE. NO APPARENT CONFLICT.

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ON THE EVENING OF JUL/TUE/97 I WAS THE PF FROM SFO TO LAX. WHILE ON DOWNWIND FOR AN EXPECTED VISUAL APCH TO RWY 24R AT LAX AT AN ALT OF APPROX 5000 FT MSL DSNDING TO 2500 FT MSL WE WERE INSTRUCTED TO TURN BASE AND ADVISED OF B767 TFC FOR THE 'S COMPLEX.' WE RPTED THE TFC IN SIGHT AND THE CAPT AND MYSELF CONCURRED WE WOULD BE PARALLEL TO AND BEHIND THAT ACFT. SUBSEQUENTLY; WE WERE ADVISED OF ADDITIONAL TFC (I BELIEVE A BRASILIA OR SAAB) TO FOLLOW FOR THE VISUAL. WE RPTED THAT TFC IN SIGHT AS WELL AND WERE CLRED FOR THE VISUAL APCH TO RWY 24R. THE CAPT ASKED ME TO CONFIRM I HAD THE RWY IN SIGHT AND WHILE ATTEMPTING TO VERIFY MY RWY I LOST THE COMMUTER TFC. I QUICKLY REACQUIRED THE COMMUTER; BUT WHEN I LOOKED BACK TO THE RWY I FOCUSED ON RWY 25R. I BELIEVE; IN HINDSIGHT THE SHALLOW ANGLE DOGLEG I WAS USING TO PREVENT A POSSIBLE OVERSHOOT CONTRIBUTED TO MY ILLUSION. AS I CROSSED TO THE S SIDE OF RWY 24L THE CAPT ALERTED ME OF THE SIT AND WE IMMEDIATELY CORRECTED BACK TO THE CTRLINE OF OUR ASSIGNED RWY. AT NO TIME DID WE RECEIVE A TCASII WARNING AND WE HAD THE B767 IN SIGHT THROUGHOUT. TOTAL TIME S OF RWY 24R CTRLINE WAS APPROX 12-15 SECONDS.