B737-500 CREW HAD TRACK DEV WHILE FLYING THE LYNSY 2 RNAV APCH INTO LAS.

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LYNSY 2 ARR TO LAS AT 12000 FT MSL; 250 KIAS. JUST PAST LYNSY; ACFT TURNED TO MIROK. LAS APCH SAID YOU ARE CLRED DIRECT UTARE. THIS WILL PUT YOU BACK ON THE ARR. LNAVE SHOWED ON COURSE. WE PRECEEDED DIRECT TO UTARE. I ASKED THE CTLR IF HE SHOWED US ON COURSE. HE SAID WE WERE ABOUT 3 MI W OF TRACK. AT THIS TIME; I TOLD THE CTLR WE WERE HAVING A NAV PROB AND WOULD NEED VECTORS. HE GAVE US A HDG TO FINAL; AND WE LANDED UNEVENTFULLY. AT NO TIME DID WE GET A 'UNABLE NAV RWP;' AND THE SYS CHKED GOOD. END OF RWY FIX SEEMED TO BE RIGHT ON; AND CURRENT POS AND GATE COORDINATES WERE WITHIN 1 MI. SYS WAS UPDATED CORRECTLY IN OUR DEPARTING CITY; AND THE SWITCHES WERE IN THE CORRECT POS ON THE ARR. I REALLY HAVE NO IDEA WHY THE ERROR OCCURRED. THE FLT FLEW OPS NORMAL ON RETURN TRIP. TFC WAS LIGHT INTO LAS; AND THERE WERE NO PROBS WITH APCH CTL. I WISH I COULD GIVE YOU MORE; BUT I REALLY DON'T KNOW WHY IT HAPPENED. SUPPLEMENTAL INFO FROM ACN 583924: THE CAPT AND I DISCUSSED WHAT MAY HAVE CAUSED THIS PROB. WE ARE SURE; DUE TO LONG DELAYS; THAT THE FMC WAS PROGRAMMED WITH THE CORRECT RWY AND UPDATED PROPERLY. LNAV WAS ENGAGED ON THE ARR; BECAUSE THE ACFT WAS TURNING AT WHAT WE BELIEVED WERE THE CORRECT FIXES. THE LNAV DID NOT SHOW A LARGE POS ERROR ON THE GND IN LAS.