B767 FLT CREW HAS PROGRAMMED FMC AND IS FLYING ARR FOR RWY 25R. AFTER CHANGING FREQS TO FINAL APCH CONTROL; THIS CTLR INSISTS THEY WERE GIVEN RWY 24R AND GAVE THE FLT CREW A VECTOR TO INTERCEPT RWY 24R LOC.

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I WAS THE FO AND PF. PRIOR TO THE TOP OF DSCNT; THE ATIS AT LAX SAID RWY 25L CLOSED; LNDG RWY 25R ON THE SOUTH COMPLEX. WE LATER CONFIRMED THIS ON THE COPY OF THE ATIS WE HAD EARLIER PRINTED OUT FROM THE ACARS. WE SETUP AND BRIEFED FOR AN ILS RWY 25R. THE CAPT CHKED IN WITH APCH WELL INTO THE DSCNT AND ALREADY ON THE SEAVU ONE ARR. WE THOUGHT WE WERE ASSIGNED RWY 25R AS WE HAD HEARD ON THE ATIS AND BRIEFED. LATER WE WERE HANDED OFF TO THE NEXT APCH CTLR. SOMETIME AFTER MAKING THE TURN AT LUVYN; WHICH IS OVER 40 MILES FROM THE ARPT; THE CTLR SAID WE WERE SUPPOSED TO BE GOING TO RWY 24R. THE CAPT STATED WE HAD BEEN GIVEN RWY 25R; BUT THE CTLR INSISTED THE PREVIOUS CTLR HAD GIVEN US RWY 24R AND THAT RWY 25R WAS CLOSED. THE CTLR THEN GAVE US A SLIGHT R TURN TO INTERCEPT THE RWY 24R LOC. I DON'T KNOW IF WE HEARD WHAT WE EXPECTED TO HEAR OR IF WE WERE IN FACT GIVEN RWY 25R BY THE INITIAL CTLR. I DO KNOW HOWEVER THAT THE ATIS THAT WAS BROADCAST A FEW MINUTES EARLIER STATED RWY 25L CLOSED; LNDG RWY 25R. NOW IF A RWY CLOSES THAT THE ATIS HAD JUST RECENTLY BROADCAST AS THE LNDG RWY; THEN THE CTLR NEEDS TO MAKE ABSOLUTELY SURE EVERYONE IS ON THE SAME PAGE WHEN IT COMES TO RWY ASSIGNMENTS. WE ARE RESPONSIBLE FOR ALL AVAILABLE INFORMATION; HOWEVER WE NEED THAT INFORMATION TO BE TIMELY AND CORRECT. WE CANNOT LISTEN TO THE ATIS EVERY 5 MINUTES WHILE FLYING THE ACFT DURING DSCNT; APCH; AND LNDG; AS THIS IS A VERY HIGH WORKLOAD TIME. IF SOMETHING AS CRITICAL AS A RWY CLOSING HAS JUST HAPPENED THEN ATC NEEDS TO ENSURE WE ARE AWARE AND NEEDS TO LISTEN CAREFULLY TO READBACKS.