C560 CREW HAD A METRO LINER CUT IN FRONT OF THEIR ACFT AFTER THEY WERE CLRED FOR TKOF AT LIT.

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AFTER COMPLETING OUR TAXI TO RWY 18 AT LIT; WE WERE CLRED FOR TKOF. WE THEN STARTED OUR FINAL BEFORE TKOF CHKLIST ITEMS. AFTER MAKING THE TURN IN POS AND BEFORE I ADVANCED THE THROTTLES I NOTICED A METRO LINER TAXIING RAPIDLY FROM THE RAMP TOWARDS RWY 18 ON TXWY B. I SAID TO THE FO; I DON'T THINK HE'S GOING TO STOP. THE FO THEN SAID I THINK YOU'RE RIGHT. THE ACFT THEN CROSSED OUR RWY. THE FO THEN QUESTIONED THE TWR AND THEY CONFIRMED THAT WE WERE CLRED FOR TKOF AND THE METRO LINER WAS CLRED TO RWY 18 NOT RWY 22R. THE METRO LINER THEN RESPONDED THAT HE; IN FACT; WAS CLRED TO 'TAXI UNRESTR TO RWY 22R.' THE TWR DISAGREED. AFTER LNDG AT OUR HOME BASE I CALLED THE LIT TWR TO TALK WITH THEM ON WHAT EXACTLY HAPPENED. THE SUPVR SAID HE WOULD LISTEN TO THE TAPE AND LET ME KNOW. WHEN HE CALLED ME BACK HE SAID THE CTLR DID IN FACT CLR THE AIRPLANE TO RWY 22R INSTEAD OF RWY 18. THE SUPVR THEN THANKED ME FOR OUR PART IN AVOIDING A SERIOUS INCIDENT. SOME THINGS TO THINK ABOUT. 1) WHEN CLRED FOR TKOF; MAKE SURE YOU'RE CLR. 2) IF YOU ARE APCHING A RWY AND SEE AN ACFT IN POS WITH ITS LNDG LIGHTS ON; YOU SHOULD ASSUME IT'S BEEN CLRED FOR TKOF AND NOT CROSS THE RWY WITHOUT CONFIRMATION. 3) DON'T TAXI SO FAST!