B737-300 CAPT DESCRIBED INCIDENT ON DEP FROM LAX WHEN TKOF ATC RWY CROSSING CLRNC WAS HEARD DURING TKOF CAUSING NEAR ABORT.

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THIS WAS THE LAST LEG OF A 4 DAY TRIP FROM LAX. WE WERE CLRED FOR TKOF FROM THE CONCRETE PAD AT LAX FOR RWY 24L. AS WE TAXIED ONTO THE RWY; I XFERRED ACFT CTL TO MY FO AND WE BEGAN THE TKOF ROLL. ABOUT THIS TIME; I HEARD ON THE RADIO 'ANOTHER CARRIER CLRED TO CROSS RWY 24L; HOLD SHORT OF...' I DIDN'T FULLY HEAR THE CLRNC GIVEN TO THE OTHER ACFT SINCE THIS WAS A BUSY TIME (TAXIING THE ACFT ONTO THE RWY; XFER OF ACFT CTL; ETC). HOWEVER; I DEFINITELY HEARD ANOTHER ACFT CLRED TO CROSS MY RWY. I IMMEDIATELY LOOKED UP AND SAW 2 ACFT HOLDING SHORT OF RWY 24L DOWNFIELD. MY INITIAL THOUGHT WAS I NEED TO ABORT (WE WERE AT ABOUT 60 KIAS) BECAUSE ONE OF THESE ACFT IS GOING TO TAXI ACROSS MY RWY DURING THIS TKOF. I WAS ABOUT TO INITIATE THE ABORT WHEN I REMEMBERED THAT THERE WAS ANOTHER CARRIER'S BRASILIA ON THE PARALLEL TXWY WHEN WE WERE CLRED FOR TKOF. I THEN REALIZED THAT HE WAS CLRED TO CROSS RWY 24L BEHIND ME. HOWEVER; I ALSO KEPT A CLOSE EYE THE 2 ACFT HOLDING SHORT DOWNFIELD. THE TKOF WAS COMPLETED WITHOUT INCIDENT. THE BEGINNING OF THE TKOF ROLL IS A BUSY TIME. WE ARE TAXIING THE ACFT; XFERRING CTL; AND SETTING TKOF PWR. THOUGH I AM LISTENING ON THE RADIO; IT IS NOT MY ONLY FOCUS. TWR SHOULD HAVE LET US KNOW THAT THEY WOULD BE TAXIING THE BRASILIA ACROSS BEHIND US. I WAS REAL CLOSE TO ABORTING MY TKOF BECAUSE OF THAT RADIO CALL. IT'S VERY UNNERVING TO HEAR AN ACFT CLRED TO CROSS A RWY YOU WERE JUST CLRED FOR TKOF FROM.