A B733 CREW; DESCENDING INTO KLAS; RECEIVED A CLIMB 'RA' FROM TCAS. WITH THE TFC IN SIGHT A DESCENDING TURN WAS INITIATED TO MAINTAIN SEPARATION.

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LA CENTER CLRED US TO DSND VIA THE LYNSY ONE ARRIVAL. WE WERE DSNDING ON SPD AS TO CROSS LYNSY AT 12000 FT MSL; 250 KTS. NAV WAS IN ACCORDANCE WITH COMPANY RNAV ARRIVAL PROCS. 11-12 NM PRIOR TO LYNSY; LA CENTER ADVISED US THAT THERE WAS A CITATION AT 13500 FT MSL; JUST NORTH OF LYNSY; AND THAT HE WAS TALKING TO LAS APCH. BOTH THE CTLR AND MY COCKPIT CREW BELIEVE THAT CITATION WOULD STAY AT 13500 FT MSL. ABOUT 4-5 NM FROM LYNSY; THE CTLR INFORMED US THE CITATION WAS DSNDING AD CLRED US TO 11000 FT MS. TCAS FIRST SHOWED THE CITATION LEVEL AND CONTINUED TO SHOW HIM LEVEL EVEN AFTER THE CTLR CALLED OUR DSCNT. WE EXPEDITED THE DSCNT TO 11000 FT. THE CTLR THEN INSTRUCTED US TO DSND TO 10000 FT. THE FO WAS FLYING. HE INCREASED DSCNT TO 2500 RPM. TCAS NOW SHOWED THE CITATION ON THE NOSE TO SLIGHTLY RIGHT ABOUT 3 NM; ABOVE US; DSNDING. WE BOTH WENT OUT TO ACQUIRE THE CITATION. THE FO ACQUIRED THE CITATION VISUALLY ABOVE US; CLOSING ON A COLLISION COURSE AT ABOUT THE 12:30 O'CLOCK POS. HE CHECKED THE AUTOPLT OFF; STARTED A RIGHT TURN ABOUT 1 NM PRIOR TO LYNSY; AND SMOOTHLY INCREASED THE DSCNT RATE WITH THE CITATION PASSING RIGHT TO LEFT ON THE NOSE; ABOVE US; BY ABOUT 300 FT; 2-1.5 NM; THE TCAS ALERTED WITH AN RA TO CLB. SINCE WE HAD A VISUAL AND WERE ALREADY IN A DSNDING EVASIVE MANEUVER ASSURED TO RECONFLICT; WE CONTINUED TO DSND AND TURN TO HIS 6 O'CLOCK POS. HAD WE FOLLOWED THE RA; WE WOULD HAVE PASSED THROUGH HIS ALT VERTICALLY; AT 12 O'CLOCK; WITHIN 0.5 NM; AND LOST SIGHT. LA CENTER THEN HANDED US OFF TO LAS APCH. LAS APCH CLRED US OFF THE RNAV RTE AND TO 8000 FT MS. COMBINATION OF EVENTS: TWO DIFFERENT ACFT; IN APPROX SAME AIRSPACE; TWO DIFFERENT CTLRS. LAX PREDISPOSED TO KEEP ACFT ON ARRIVAL RTE OVER FIX VERSES VECTOR OFF CITATION WAS VFR; TOLD LAS APCH HE WANTED TO PROCEED ON HIS OWN NAV; STARTED DSND ON HIS OWN (HE TOLD LAS HE HAD US IN SIGHT). NEW ARRIVALS TAKE IFR TFC OVER VFR SIGHT SEEING CORRIDOR. SUPPLEMENTAL INFO FROM ACN 533324: I WAS THE PLT FLYING AND INCREASED MY RATE OF DSCNT FROM 14000 FT TO 12000 FT TO MET LYNSY RESTRICTIONS EARLY (250 KTS/12000 FT). VFR ACFT APPEARED TO BA A CITATION PASSING APPROX 200 FT ABOVE AND 2000 FT TO 3000 FT SOUTHWEST OUR POS. THE CAPT CONTACTED SUPVRS FOR LA CENTER AND APCH CTL. PER ACR FOM CAPT THEN CONTACTED OUR CHIEF PLT. WE BOTH FEEL THERE IS A POTENTIAL PROB WITH THE NEW RNAV ARRIVAL AND VFR ACFT TRANSITING A NORTH/SOUTH RTE ALONG THE COLORADO RIVER. APPARENTLY THIS PARTICULAR ACFT HAD BEEN UNDER THE CTL OF LAS APCH AND CANCELLED IFR. HE CLAIMS OR TOLD APCH HE HAD VISUAL WHEN WE WERE HEAD ON WITH OUR PULSATING LNDG LIGHTS ON. THERE APPEARS TO BE A POTENTIAL CONFLICT WITH IFR COMMERCIAL TFC ARRIVING VIA THE LYNSY RNAV 1 TO LAS AND VFR TFC TRANSITING ALONG THE COLORADO RIVER AT MID LEVEL ALTS (10000 FT TO 15000 FT).