ACR ON TKOF AT LAX RWY 24L DESCRIBED GND CONFLICT AS ACFT LNDG ON PARALLEL RWY 24R FAILED TO HOLD SHORT OF DEP RWY.

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CLRED FOR TKOF ON RWY 24L. HEARD TWR ISSUE RWY HOLD SHORT INSTRUCTIONS TO ACFT LNDG ON RWY 24R. LNDG ACFT APPEARED TO SLOWLY ADVANCE TOWARD THE HOLD SHORT POS AS EXPECTED. LNDG ACFT HAD ITS LIGHT ON AND WAS GENERALLY VISIBLE DURING OUR TKOF ROLL. AS OUR TKOF ADVANCED; LNDG ACFT CONTINUED SLOW MOVEMENT. NOTED MOVEMENT WITH FO AND DIRECTED HIM TO KEEP AN EYE ON THE ACFT. AT THIS POINT; WE WERE WELL PAST 80 KTS AND UNABLE TO ABORT AND STOP SHORT OF THE POSSIBLE XING POINT. DISPLACED OUR ACFT SLIGHTLY L OF CTRLINE TO ALLOW FOR MAX WINGTIP CLRNC. OUR TKOF WAS 26K PWR WITH STANDARD THRUST. CONTEMPLATED FIRE WALLING THROTTLES AND EARLY ROTATION. FURTHER ACTION WAS NOT REQUIRED. PERFORMED NORMAL ROTATION AND TKOF WITH TPS PWR SETTING. AFTER LIFTOFF; HEARD LAX TWR ISSUE IMMEDIATE CANCELLATION OF TKOF CLRNC TO THE ACFT BEHIND US. DIRECTIVE WAS BROADCAST TWICE; THEN THE ACFT HOLDING SHORT OF RWY 24L CALLED TWR TO ADVISE THAT THEY MAY HAVE CROSSED THE HOLD LINE WHILE HOLDING SHORT. THOUGH LNDG ACFT WAS VISIBLE AS TO GENERAL LOCATION AND MOVEMENT; I WAS UNABLE TO DISCERN ACTUAL POS OF THE NOSE OF THE ACFT IN RELATION TO THE HOLD SHORT LINE.