RWY INCURSION CREATES NECESSITY FOR ANOTHER COMMUTER ACR TO ABORT TKOF. UNAUTHORIZED UNCOORD RWY ENTRY XING.

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I WAS INSTRUCTED TO HOLD SHORT OF 25R (AT 42). TWR CTL SAID SOMETHING I THOUGHT WAS FOR OUR ACFT. I ASKED MY FO TO CLARIFY WHAT THEY HAD SAID. 'THEY SAID WE ARE CLRED TO CROSS 25R'. I THEN INSTRUCTED HIM TO LOOK UP THE RWY 25R AND MAKE CERTAIN IT WAS CLR. MY FO RESPONDED TO GND CTL '1236 CLRED TO CROSS 25R'. AFTER TURNING TO HIS R; LOOKING UP THE RWY; MY FO STATED 'I DON'T SEE A THING'; SO WE CROSSED 25R. AFTER DOING SO; I WAS INSTRUCTED TO TELEPHONE THE TWR. WHEN I TALKED TO THE SUPVR HE TOLD ME THAT XMISSION TO CROSS 25 R WAS FOR AN ACR WITH ALMOST IDENTICAL CALL SIGN TO OURS. THE TWR SUPVR ALSO TOLD ME THAT THERE WAS AN ACR LTT WHO HAD TO ABORT HIS TKOF ROLL. I; IN TURN; TOLD THE SUPVR WHAT HAD HAPPENED FROM OUR END AND THAT WE WERE SORRY ABOUT THE MIX-UP. SUPPLEMENTAL INFO FROM ACN 189098: THE ONLY CHANGE IN OUR ACTIONS WHICH COULD HAVE PREVENTED THIS SITUATION WOULD HAVE BEEN FOR ME TO ASK TWR TO CONFIRM THE CALL WAS FOR OUR FLT; NECESSITATING A REPEAT OF THE INSTRUCTIONS BY TWR -- A THIRD VERBALIZATION. LAX TWR COULD HAVE ASSISTED IN PREVENTING THIS SITUATION BY: 1) IF NO RESPONSE RECEIVED FROM THE ACFT ADDRESSED; QUERYING THEM OR REPEATING INSTRUCTIONS TO THEM (AS IS NORMAL PRACTICE AT LAX). THIS WAS NOT DONE HERE; AND OTHER INSTRUCTIONS CONTINUED TO BE GIVEN TO OTHER ACFT. DUE TO CONGESTION AND TFC; LITTLE TIME WAS AVAILABLE; IF ANY; FOR RESPONSES. POSSIBLY TWR COULD HAVE SLOWED DOWN ALL OPS WHICH WOULD ENHANCE COMS AND SAFETY. 2) IF A WRONG ACFT RESPONDED TO TWR INSTRUCTIONS; IMMEDIATE CORRECTION COULD HAVE BEEN MADE; I.E.; NEGATIVE; HOLD SHORT; ETC. (NORMAL PRACTICE AT LAX.) NEITHER OF THE ABOVE NORMAL PRACTICES WERE DONE IN THIS SITUATION WHICH CONTRIBUTED TO ANY POTENTIAL SAFETY COMPROMISE.