A B757-200 MISSED THE LAX REEDR3 STAR TURN AT REEDR INTXN AFTER A VECTOR OFF THE ARR AND A RWY CHANGE REQUIRED AN FMS PROGRAMMING CHANGE.

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DESCENDING INTO LAX ON AUTOPLT DURING MODERATE TURB AND USING A STAR I'VE NEVER USED BEFORE ENRTE TO A RWY NEITHER THE FO NOR I HAVE EVER LANDED ON (RWY 7L); WE FAILED TO TURN AND TRACK OUTBOUND FROM REEDR INTXN. THE ACFT CONTINUED ON PREVIOUS HDG AND DID NOT MAKE THE TURN. APCH CTL ASKED OUR HDG; AND BEFORE WE COULD ANSWER HIM; HE VECTORED US IN THE DIRECTION WE SHOULD HAVE BEEN GOING. NO CONFLICT OCCURRED. CONTRIBUTING FACTORS INCLUDE A VECTOR OFF THE STAR A FEW MINUTES EARLIER; THE CLRNC TO A FIX ON THE STAR THAT WAS PART OF ANOTHER TRANSITION. THEN WE WERE CLRED TO CONTINUE THE STAR FROM THAT FIX. WHEN APCHING THE TURN POINT WE MISSED; APCH CTL CHANGED OUR RWY ASSIGNMENT. PF RESELECTED THE RWY ON THE FMS AND APPARENTLY THE LNAV DROPPED OUT WHEN HE DID SO. THE DISTRACTION OF THE NEW STAR; MODERATE TURB; RECLEARANCE TO A DIFFERENT TRANSITION AND FINALLY A LAST MINUTE CHANGE ALL CONTRIBUTED TO THIS EVENT. WHY CAN'T APCH CTL IN LAX STICK TO THEIR ORIGINAL PLAN? WITH FMS PROGRAMMING; GOING INTO LAX IS ALMOST ALWAYS A GOAT ROPE! ONE OF THESE DAYS THESE CONTINUAL LAST MINUTE CHANGES MAY CAUSE A SERIOUS CONFLICT.