This isn't a spoiler because it's long gone in the TV series, but was covered more fully in the books, I think (I haven't read past the second book, so don't worry...) - LF rose in the ranks so quickly *because* he was such an effective master of coin. For example, he invested in commodities on behalf of the crown and was integral in stopping King Robert from going under beneath the weight of his drinking and whoring.

The real financial problems started when LF left the post and Tyrion was given multiple wars and a wedding to pay for.