ACR MLG CROSSED RWY AS CLRED THEN SAW A COMMUTER SMT ABORT TO PREVENT GND CONFLICT.

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OUR AIRPLANE WAS TAXIING FROM THE TERMINAL FOR TKOF ON RWY 30 AT LGB. DUE TO CONSTRUCTION; WE WERE INSTRUCTED TO INCREASE OUR TAXI SPD AND CROSS RWY 30 AT INTXN JULIET; AS THERE WAS A COMMUTER ON A 3 MI FINAL. AS WE WERE ABOUT TO CROSS THE RWY; WE NOTICED AN AIRPLANE AT THE DEP END OF RWY 30; BUT IT DID NOT APPEAR TO BE MOVING. AS WE TAXIED ACROSS THE RWY; IT NOW BECAME APPARENT THAT THE AIRPLANE HAD BEEN CLRED FOR TKOF. THE ACFT ABORTED HIS TKOF. AVERTING THE POTENTIAL CONFLICT. APPARENTLY WHAT HAPPENED WAS THAT THE GND AND TWR CTLRS WERE NOT COORDINATING PROPERLY; AND CONFLICTING CLRNCS WERE ISSUED. SOLUTION: PROPER TWR COORD AND A LITTLE BETTER VIGILANCE ON MY PART. CONTRIBUTING FACTOR: THE SMT ON THE RWY DID HAVE HIS LNDG LIGHTS TURNED ON BUT DID NOT APPEAR TO BE MOVING. HERE AT COMPANY AIRLINES; IT IS PROC TO LEAVE THE LIGHTS OFF UNTIL CLRED FOR TKOF; INDICATING THE TKOF ROLL HAS BEGUN. HOWEVER; THIS IS NOT A STANDARDIZED POLICY THROUGHOUT THE INDUSTRY; CORPORATE OR GA. IF IT WAS MANDATED BY REG THAT LNDG AND TAXI LIGHTS WERE TO REMAIN OFF ON AN ACFT IN POS ON THE ACTIVE RWY; UNTIL CLRED FOR TKOF; IT WOULD ACCOMPLISH 2 THINGS: 1) IT WOULD CONFIRM TO THE TWR PERSONNEL THAT THE CLRNC HAD BEEN RECEIVED. 2) IT WOULD BE A CLR INDICATION TO OTHER ACFT THAT THE AIRPLANE IN QUESTION WAS IN MOTION.