FLC OF A B737-300 ON APCH TO LAX HAS HDG AND ALT CHANGES THEN IS INFORMED THAT A COMPANY ACFT WILL BE ON THE PARALLEL RWY AND THEY MUST MAINTAIN SPD BUT NOT PASS THE OTHER ACFT. THEY MAKE EFFORTS; BUT DO COME UP ADJACENT TO THE OTHER ACFT.

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WHILE FLYING A SCHEDULED FLT FROM PHX TO LAX; I NOTICED THAT ATC WAS MAKING NUMEROUS MODIFICATIONS TO THE CLRNC; IE; CHANGES IN ALT; HDGS; AIRSPD; ARRS; AND RWYS. WHILE INITIALLY ON A PDZ 2 TO LAX; WE WERE MODIFIED TO A MITTS 1. WE WERE ALSO ADVISED TO MAINTAIN 250 KTS ON APCH AS LONG AS POSSIBLE; BUT AT LEAST TO THE MARKER OF RWY 24L. WE WERE ADVISED OF COMPANY TFC THAT WOULD BE LNDG ON RWY 24R. WE WERE TOLD TO MAINTAIN MAX FORWARD SPD; BUT NOT TO PASS COMPANY ON FINAL APCH. I PICKED UP THE TFC LATE AND FAILED TO NOTICE THE GEAR COMING DOWN ON THE COMPANY ACFT. THEREFORE MY SPD REDUCTION WAS LATE AND AN EXCESSIVE CLOSURE RATE RESULTED. THE APCH ENDED WITH A NORMAL LNDG ON RWY 24L AND AN UNEVENTFUL TAXI TO THE GATE. I BELIEVE THAT THE NUMEROUS CHANGES REQUIRED OF US BY ATC DURING THE APCH; COUPLED WITH THE LATE RECOGNITION OF THE COMPANY ACFT ON APCH FOR RWY 24R; LED TO A SIT WHERE OUR 2 ACFT ACHIEVED A PROX THAT MAY HAVE CAUSED CONCERN BY SOME OF THE PAX ON EITHER ACFT. I DO NOT FEEL THERE WAS ANYTHING UNSAFE THAT OCCURRED DURING THE APCH.