A B737 DEVIATED FROM CHARTED VERTICAL AND LATERAL TRACKS AFTER RECEIVING A CLOSE IN RWY CHANGE ON ARR TO LAX.

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CAPT WAS PF. ON RIIVR ONE STAR TO LAX. FROM ATIS INFO FOR LAX WE PLANNED ON AND BRIEFED THE APCH FOR RWY 25L AND PUT IT IN THE FMS. SOCAL APCH TOLD US TO PLAN ON RWY 24R BUT THE NEXT CTLR MAY GIVE US RWY 25L. WE WERE GETTING CLOSE TO THE RIIVR INTXN AND REALIZED WE WERE NOT GOING TO GET RWY 25L AND STARTED TO CHANGE THE RWY AND TRANSITION IN THE FMS. AT THAT TIME WE WERE GIVEN A FREQUENCY CHANGE. BY THE TIME WE GOT THE FMS PROGRAMMED WE WERE OFF LATERALLY AND VERTICALLY ON THE STAR FOR THE RWY 24R TRANSITION. CHKED IN WITH THE NEW CTLR AND EXPLAINED WHAT HAD HAPPENED; THAT WE WERE SET UP FOR RWY 25L AND JUST GOT SWITCHED AND SET UP FOR RWY 24R AND WE WERE GETTING REESTABLISHED ON THE CORRECT TRANSITION AND DOING OUR BEST TO COMPLY WITH THE RESTRS. CTLR SAID OK AND ASKED IF WE WANTED TO SWITCH BACK TO RWY 25L. WE SAID NO AND STAYED ON THE APCH FOR RWY 24R. THE CTLR CLRED US FOR THE APCH AND THE REST OF THE FLT WAS UNEVENTFUL. WE HAD TAKEN OFF ALMOST 6 HRS PRIOR. FIRST LEG FLOWN THAT DAY AND AS A CREW. LAST MIN CHANGE OF RWY AND EXPECTATION OF LNDG ON A DIFFERENT RWY. ALL OF THESE THINGS CONTRIBUTED TO THE SLOW SWITCH OVER AND PROGRAMMING OF THE FMS. DID THE BEST WE COULD IN THE TIME ALLOWED AND EXPLAINED THE SITUATION TO ATC SO THEY WOULD KNOW WE WERE TRYING TO GET ESTABLISHED ON THE ASSIGNED STAR TRANSITION.