A HAWKER 800 XP FT CREW BECOMES DISORIENTED WHEN THE TWR CTLR ISSUES A LATE TURN ONTO FINAL AND THEY INITIALLY LINE OFF FOR THE WRONG RWY.

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FLYING INTO LAX THAT AFTERNOON; WE WERE TOLD TO EXPECT THE ILS RWY 24R. APCH CTL GAVE US A 90+ DEG HDG CHANGE TO INTERCEPT THE LOC. THE FLT DIRECTOR HAS A TENDENCY TO LAG OR SHOW INCORRECT GUIDANCE OCCASIONALLY ON SUCH SEVERE; TIGHT INTERCEPTS. WE WERE HANDED OFF TO TWR AND ASKED IF WE HAD THE FIELD VISUALLY. I RESPONDED THAT WE HAD VISUAL CONTACT WITH THE FIELD AND WE WERE CLRED FOR THE VISUAL. I STARTED TO NOTICE L DEV AND BEGAN TO CORRECT FOR THE SIT. ABOUT THAT TIME; THE TWR CTLR BEGAN TO QUESTION OUR POS RELEVANT TO OUR LNDG RWY. I BECAME CONFUSED AND BELIEVED HE WAS REFERRING TO RWY 25R WHICH I HAD IN SIGHT. I INCORRECTLY BEGAN TURNING L; MISTAKING RWY 25R FOR RWY 24R. TWR CAME BACK AND ORDERED AN IMMEDIATE R TURN AT WHICH TIME RWY 24R WAS JUST COMING INTO VIEW. IT WAS VERY HAZY AND VISIBILITY WAS NOT GOOD LOOKING INTO THE BRIGHT SETTING SUN. I MADE THE CORRECTION AND WE LANDED WITHOUT ANY OTHER PROBS. TWR AND GND NEVER TOLD ME TO MAKE ANY PHONE CALLS OR ACTION REQUIRED. I SHOULD HAVE STUCK TO THE INSTS INSTEAD OF RELYING ON TRYING TO VISUALLY IDENTIFY RWY 24R. I ALSO BELIEVE THE APCH CTLR DID NOT HELP US OUT BY GIVING US A LATE TURN ON; JUST OUTSIDE THE FAF; WITH A 90+ DEG INTERCEPT HDG CHANGE. I BELIEVE IF HE HAD GIVEN US MORE STANDARD INTERCEPT GUIDANCE; I WOULDN'T HAVE HAD ANY PROB INTERCEPTING THE LOC OR DOUBTING THE FLT DIRECTOR -- WHICH DOES LAG AND GIVE INCORRECT COURSE GUIDANCE DURING AGGRESSIVE MANEUVERING. THE LOC WAS READING ACCURATELY THOUGH. I DID BECOME CONFUSED MOMENTARILY BTWN MY VISUAL PICTURE; INST INDICATION; AND TONE OF TWR CTLR'S VOICE AND QUESTIONING. DEFINITELY LEARNED A VALUABLE LESSON.