B727 HAS DIFFICULTY FLYING VISUAL APCH TO RWY 24R AT LAX BECAUSE OF WX.

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WE WERE CLRED BY LAX APCH CTL TO DEPART SANTA MONICA ON A 070 DEG HDG AS A VECTOR FOR AN ILS APCH TO RWY 24R AT LAX. APPROX 5 MI E OF THE ARPT THE CTLR ASKED WHETHER WE HAD THE ARPT IN SIGHT. WE ADVISED THAT WE DID. HE THEN CLRED US TO FOLLOW AN ACFT THAT WAS ON FINAL FOR RWY 24R AND CLRED US FOR A VISUAL APCH TO RWY 24R. I TOLD THE FO (WHO WAS FLYING) TO TURN TO A 180 DEG HDG. AS WE TURNED BASE WITH THE ACFT AHEAD IN SIGHT; DUE TO MARGINAL VISIBILITY WE LOST VISUAL CONTACT WITH THE RWY. DURING THE TURN TO FINAL AND AFTER CONTACTING THE TWR CTLR; WE FLEW SLIGHTLY THROUGH THE LOC COURSE. THE TWR CTLR ADVISED US THAT PARALLEL APCHS TO RWY 25L WERE IN PROGRESS AND REQUESTED US TO TURN BACK N TO INTERCEPT THE LOC. I ADVISED THAT WE WERE IN THE R TURN TO INTERCEPT. WE CONTINUED THE APCH AND LNDG WITHOUT INCIDENT. NO TFC CONFLICTS OCCURRED AT ANY TIME DURING THE APCH. I THINK THE PROB WAS CAUSED BY THE FOLLOWING FACTORS: 1) ME BEING DISTR FROM OUR POS IN RELATION TO THE LOC WHILE TRYING TO REGAIN VISUAL CONTACT WITH THE RWY. 2) MY CONCENTRATING ON TRYING TO MAINTAIN VISUAL CONTACT WITH THE ACFT AHEAD. 3) MARGINAL VISIBILITY CONDITIONS; WHICH PREVENTED OUR ABILITY TO MAINTAIN VISUAL CONTACT WITH THE RWY (WHICH WE HAD EARLIER). I THINK THE PROB CAN BE AVOIDED IN THE FUTURE BY REFUSING TO ACCEPT A VISUAL APCH IN MARGINAL CONDITIONS. SUPPLEMENTAL INFO FROM ACN 339781: WE FLEW THROUGH THE RWY 24R LOC AND WAS LINED UP WITH RWY 24L. REALIZING OUR MISTAKE WE CORRECTED BACK TO RWY 24R ABOUT THE SAME TIME THE CTLR ASKED IF WE WERE CORRECTING BACK. WE LANDED WITHOUT INCIDENT. THIS EVENT COULD HAVE BEEN AVOIDED IF WE DID NOT ACCEPT A VISUAL APCH IN MARGINAL CONDITIONS.