LTT COMMUTER ACFT IS VECTORED TO APCH ON RWY 24L BEHIND A B737 ON APCH TO RWY 24R. CLRED FOR VISUAL WITH STIPULATION THAT THEY KEEP THE ACFT IN SIGHT AND DO NOT PASS THE B737. THE B737 GETS A TCASII RA.

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RPTED WX LAX 1000 FT BROKEN; VISIBILITY 9 MI; THE BROKEN LAYER WAS OVER THE ARPT; BUT ONLY EXTENDED APPROX 2 MI TO THE E OF THE FIELD. BEYOND THAT THE LAYER ENDED; YIELDING TO CLR SKIES. I WAS CAPT ON FLT FROM SBP TO LAX AND THE PF. WE WERE ON A DOWNWIND VECTOR OF HDG 070 DEGS N OF LAX'S N RWY COMPLEX. AN AIRLINE B737 WAS AHEAD IN SEQUENCE AND ON BASE LEG FOR LAX RWY 24R; SOCAL CALLED THIS TFC TO US AND INFORMED US IF WE COULD KEEP THE ACFT IN SIGHT WE WOULD GET A VISUAL TO RWY 24L. WE CALLED THE B737 IN SIGHT AND ACCEPTED A VISUAL APCH TO RWY 24L; WITH THE B737 LNDG RWY 24R; WITH THE STIPULATION THAT WE NOT PASS THE ACFT. WE KEPT THE B737 IN SIGHT AT ALL TIMES AND REMAINED IN VISUAL CONDITIONS AT ALL TIMES. WE MANEUVERED INTO A POS TO THE S (L) OF THE B737 AND SLIGHTLY BEHIND THEIR ACFT. BOTH ACFT WERE GIVEN A FREQ CHANGE TO LAX TWR N COMPLEX. WE CHKED ON WITH LAX TWR AND WERE CLRED TO LAND. THE B737 THEN RPTED TO TWR THAT THEY HAD AN RA AND DID NOT HAVE US IN SIGHT. TWR INFORMED THEM THAT THE ACFT WAS VISUAL ON THEM TO RWY 24L. THE B737 DISCUSSED WITH TWR GOING AROUND SINCE THEY DID NOT HAVE US IN SIGHT; AND I BELIEVE THEY STATED THEY DID NOT HAVE THE RWY IN SIGHT. DUE TO THE FACT THAT THEY WERE REACTING TO THE RA AND PERHAPS ABOVE THE GS THEIR FORWARD VISIBILITY MAY HAVE BEEN IMPAIRED. THE B737 THEN RPTED THE RWY IN SIGHT AND INFORMED TWR THEY WOULD NOT PERFORM A GAR. ALTHOUGH WE REMAINED IN VISUAL CONDITIONS AND HAD THE B737 IN SIGHT AT ALL TIMES; CONDITIONS FOR THESE TYPES OF VISUALS WERE BECOMING MARGINAL. BETTER COMS NEED TO EXIST BTWN SOCAL AND LAX TWR; INCLUDING SOLICITING PIREPS FOR THESE OPS. I ALSO DON'T BELIEVE THE B737 UNDERSTOOD FROM SOCAL THAT WE WOULD BE MANEUVERING IN THEIR VICINITY.