B737 FLT CREW HAS RWY INCURSION AT LAX.

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DAY VMC LAX. LANDED RWY 24R; CLRED TO CROSS RWY 24L TXWY Z; EXITED ON TXWY E. TOLD TO HOLD SHORT OF E13 WHILE B747 REPOSITIONED UNDER TOW. RESUMED TAXI WITH INSTRUCTIONS 'TXWY E; TXWY D10; TXWY D TO GATE.' I WROTE DOWN THE INSTRUCTIONS; READ BACK TO GND AND CAPT CONFIRMED TO ME 'TXWY E; TXWY D10; TXWY D.' I LOOKED AT CHART TO CONFIRM RTE. ABEAM TXWY W; CAPT STARTED TURNING L. I WAS SURPRISED AT THE L TURN (SHOCKED). BY THE TIME I COULD SAY ANYTHING; WE WERE ON RWY 24L. NO ACFT WERE ON APCH TO THE L OR HOLDING IN POS OR TAKING OFF. THERE WERE NO DISTRS IN THE COCKPIT. GND WAS UNUSUALLY QUIET FOR LAX (NOT MANY ACFT ON DECK). AS SOON AS HE COMMENCED THE L TURN; I SHOULD HAVE JUST SAID 'STOP.' I WAS SO SHOCKED BASED ON THE CLRNC AND MY UNDERSTANDING OF THE TAXI RTE ASSIGNED; I HESITATED MOMENTARILY THINKING THERE MUST HAVE BEEN A CALL THAT I MISSED. BY THE TIME I REALIZED WHAT WAS HAPPENING; IT WAS TOO LATE. LESSON LEARNED: ONCE THE RTE IS ASSIGNED; REVIEWED; ANY TURNS CONTRARY TO MY UNDERSTANDING OF THE RTE WILL BE CHALLENGED WITH THE WORD 'STOP!' THE EVENT WAS CAUSED BY WHAT CAN BEST BE DESCRIBED AS A 'BRAIN VOID.' CONTRIBUTING FACTOR WAS MY MOMENTARY HESITATION AND NOT CHALLENGING HIS ACTION WITH 'STOP' BASED UPON MY UNDERSTANDING OF THE ASSIGNED TAXI RTE. THERE ARE NO EXCUSES -- HE 'BRAIN VOIDED' AND I WAS TOO SLOW IN CHALLENGING HIS ACTIONS. SUPPLEMENTAL INFO FROM ACN 566298: WHEN WE ARRIVED AT E-10; I MADE A L TURN INSTEAD OF A R TURN AND IMMEDIATELY SAW THAT I HAD TAXIED ONTO RWY 24L. WE WERE THEN CLRED TO TAXI AND CLR THE RWY AT E-8 AND TAXI TO THE GATE. THERE WERE NO ACFT WAITING FOR TKOF ON RWY 24L AND 1 ACFT ON ARR FOR RWY 24R. I UNFORTUNATELY HAD THE LAY IN MY MIND THAT WE WERE ON THE INNER (D) AND THAT WE WERE TO PASS THE FACING B737 ON THE OUTER -- WRONG! THE VISUAL CUES THAT LED ME INTO THIS SIT WERE: 1) NO ACFT WAITING FOR DEP ON RWY 24L; 2) FACING THE B737 WHICH I THOUGHT WAS ON TXWY D. HAD THERE BEEN LCL ACTIVITY ON RWY 24L; I DOUBT THAT THIS EVENT WOULD HAVE OCCURRED.