B737 FLC ISSUED VISUAL APCH BUT UNABLE TO REMAIN CLR OF CLOUDS. MISSED APCH EXECUTED AND TWR CLRS TO CLB HDG 250 DEGS AND MAINTAIN 2000 FT. TCASII ACTIVATES DUE TO ACFT DEPARTING ON RWY 24L. BOTH ACFT IN CLOUDS BUT CTLR SAYS 'TFC NOT A FACTOR.'

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BACKGND: AS I REMEMBER; ATIS WAS CALLING CEILINGS 900 FT BROKEN; VISIBILITY 8 MI IN MIST; ILS IN USE AT LAX. 2 ACFT AHEAD OF US. ACR #1 ASKED SEVERAL TIMES FOR A VISUAL AND WAS GIVEN THE VISUAL APCH TO RWY 24R. SUBSEQUENT ACFT WERE VECTORED FOR AND GIVEN THE VISUAL APCH TO RWY 24R; INCLUDING OURSELVES. WE ENDED UP DOING A MISSED APCH; CAUSED BY AN UNSTABILIZED APCH DUE TO OUR EFFORT TO AVOID CLOUDS ON FINAL. OUR MISSED APCH BEGAN AT LESS THAN 500 FT AGL AND INSTRUCTIONS ISSUED BY THE TWR WERE 'FLY HDG 250 DEGS; MAINTAIN 2000 FT...' AS TCASII ENABLED ON CLBOUT; WE GOT AN RA. THE CAPT FOLLOWED THE RA GUIDANCE; REACHING AN ALT OF APPROX 2400 FT BEFORE RECEIVING THE 'CLR OF CONFLICT.' THE ACFT CAUSING THE RA WAS AN ACR #2 JET THAT HAD BEEN CLRED TO TAKE OFF RWY 24L. WE BOTH BROKE OUT OF THE CLOUDS AT APPROX 1500 FT MSL; NEAR THE COASTLINE. THE ACR #2 BEGAN A TURN TO THE L AS WE SAW EACH OTHER. WHAT CONCERNED US; BESIDES THE FACT THAT OUR CLRNC PUT US SO CLOSE TO AN ACFT TAKING OFF THAT WE RECEIVED AN RA; WAS LAX TWR'S NONCHALANT ATTITUDE. WE BOTH REMEMBER HEARING A 'TFC NOT A FACTOR CALL.' 1) HOW CAN TWR ASSURE CLRNC WHEN BOTH ACFT ARE IMC? 2) LAX PROCS ARE FOR DEPARTING ACFT NOT TO TURN UNTIL THE COASTLINE; AND TO MAINTAIN EITHER 2000 FT OR 3000 FT. IF MISSED APCH INSTRUCTIONS ARE STRAIGHT AHEAD TO 2000 FT; THIS LEAVES ONLY THE DISTANCE BTWN THE RWYS FOR ACFT SEPARATION. IT IS NOT UNCOMMON FOR A MARINE LAYER OF CLOUDS TO OBSCURE THE DEP END WHILE THE ARR END IS CLR. HENCE; WE COULD BOTH SEE THIS SAME SCENARIO HAPPENING AGAIN; WITH NO VISUAL SEPARATION BTWN ACFT THAT ARE ASSIGNED ESSENTIALLY THE SAME AIRSPACE.