Expensive lesson for The Calling's lead singer ... American Express will go wherever you will go -- especially when you STIFF 'em on tens of THOUSANDS of bucks.
TMZ obtained a copy of the lawsuit AMEX filed against Alex Band ... claiming he racked up $30,000 in debt over the last 2 years, and has refused to pay it back.
The financial giant wants its money STAT, and is suing for more than $30K ... to cover the debt and their legal fees. Band's rep hasn't gotten back to us yet.
Alex can't buy a break lately -- last year he claimed he was kidnapped, beaten and robbed by gunmen who made off with $1,200.