LESS THAN LEGAL SEPARATION ON APCH TO LAX RWY 25R-L.

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WE WERE CLRED ON A PROFILE DSCNT TO LAX RWY 25L AND ON COURSE. AT 30 DME WE WERE TOLD TO STAY ON THE RWY 25L ILS/LOC UNTIL ESTABLISHING A VISUAL WITH THE ARPT. THEN CLRED TO LAND ON RWY 25R. ACR Y JET WAS THEN CLRED FROM THE S TO LAND ON RWY 25L. THE CONDITIONS WERE VERY MURKY AND NO VISUAL CONTACT WITH THE ARPT WAS ESTABLISHED UNTIL WE BROKE OUT OF A CLOUD DECK AT 900' ON THE ILS TO RWY 25L. WE SIDESTEPPED TO RWY 25R AND LANDED. DURING THE LAST 10 MI ACR Y AND OUR FLT WERE BOTH TOLD TO REMAIN AS CLRED ON THE ILS 25L; WE COULD BOTH SEE THE OTHER'S LIGHTS RAPIDLY CONVERGING AND EXPRESSED THIS TO APCH CTL AND TWR. I SLIPPED 1 DOT RIGHT OF THE LOC TO ALLOW A BUFFER AND STILL NOT INTERFERE WITH APCHS TO THE 24 RWYS. ACR Y AGAIN ASKED APCH IF WE WERE ON THE RWY 25L LOC. NO ANSWER. WE WERE STILL IFR AND EXPRESSING CONCERN AT CONVERGING ON THE SAME LOC AND EACH OTHER THOUGH CLRED TO LAND VFR ON DIFFERENT RWYS. AT THE LAST MINUTE; APCH TOLD ACR Y TO GO AROUND. WE CONTINUED ON THE RWY 25L ILS AND SIDESTEPPED TO RWY 25R. ARPT WAS RPTING VFR. MY SUGGESTION: APCH SHOULD NOT CLR 2 ACFT TO INTERCEPT THE SAME LOC W/O SEP AND NOT BE VERY AWARE OF VIS OR RESTRICTIVE WX CONDITIONS. THIS IS ESPECIALLY TRUE IF ONE IS CLRED TO SIDESTEP FROM A NAVAID ONLY WHEN THE ARPT IS IN SIGHT.