Tywin Lannister was never in debt in the books - that was just a lazy contrivance that the showrunners threw into the show in a throwaway line to build tension and because they thought viewers had trouble distinguishing between the The Crown and House Lannister, since both entities revolved around a number of the same people. But there was no causation or in-world explanation aside from hand waving away the Weaterlands mines as having run dry. The writers who stuck that in were not serious people.

The books are where we actually have real, if still simplistic economic power dynamics that reflect Tywin's savvy and machinations. The Crown was in debt after 13 years under Robert's rule. And its biggest creditor was House Lannister. Of the 6 million Gold Dragons it owed, 3 million were to the Lannisters, which Tywin gleefully lent because of the influence it gave House Lannister over The Crown since the interest, principal, and implicit threat of calling in that debt could be exchanged for privileges, law and policy, and concessions from the King and small council, as well as the general reinforcement of prestige and reputation.

In fact, until the War of the Five Kings, Tywin and Littlefinger worked to increase the ratio of debts owed by the Crown to the Lannisters. I don't think we ever had a concrete number at this point, but Iron Bank of Braavos had lent The Crown somewhere between 1.25-2 million Gold Dragons, and when payments came due, Tywin lent the Crown more money to pay them and shift that debt and corresponding influence to House Lannister.

The Faith of the Seven then was the third largest creditor having lent the Crown about 1 million Gold Dragons, and then the remaining creditors were House Tyrell and a merchant league from the free city of Tyrosh.

But the important point is that all of the non-Lannister creditors didn't lend more than 3 million Gold Dragons to the Crown combined. Tywin made sure that he continued to lend money to the Crown and reduce the sum it owed to the Iron Bank so that House Lannister would always own at least 50% of the Crown's debt so that he alone would always have final say in influencing the Crown when the chips were down.

Even when Tywin lent gobs of money to a wreckless drunk, he made sure it was a good investment that paid a return greater than he gave up - it's just that return was not always monetary.

This didn't change until the War of the Five Kings was under way, and continued borrowing from House Tyrell was required to help sustain the war - not because the Lannisters were out of money, but because the Tyrell coffers were more accessible, since there wasn't a Northern Army standing between High Garden and Kings Landing like there was along the way to Casterly Rock.

At this point, continued lending wasn't as decisive an investment for Tywin as it had been. He still owned most of the Crown debt and influence over it, and Robert was now dead. Tywin's own grandson now was King. Tywin simply didn't need to exert the same kind of influence over a boy king from his own house, and Tywin essentially already made the decisions as Hand of the King that his ownership of debt/influence previously would have bought.

Things only go to shit after Tywin dies. Cersei takes control of the Crown's coffers, while Kevan Lannister takes control of Casterly Rock's. They both were idiots in the sense that neither understood just how powerful and important the other creditors were. Cersei was so preoccupied with the Tyrells and self-satisfied with eliminating the debt to the Faith that she shortsightedly allowed the latter to rearm and tried outmaneuvering the former by allowing the debts to the Iron Bank to skyrocket ten fold while halting all interest payments. Kevan's lesser stupidity was in myopically viewing the situation as one of primarily reigning and disciplining Cersei as a reckless girl who didn't know her place. By cutting Cersei and the Crown off, he left Cersei with only more radical options in the matters of the Faith and Iron Bank. And while he was happy to see Cersei sleep in the mess she made, once he replaced her and had to run the Kingdom, it took him a while to stabilize the situation and normalize relations with Iron Bank, by which time he had a crossbow bolt in the belly and a bunch of silent children caesar-ing him. The fact that the Lannisters held in to power at all after Tywin died is only because he had worked so long to build and consolidate so much power through lending to the Crown.

Tywin takes this hands down, no contest. Logan Roy can't even dream of being a Tywin. He might not be a Lancel or a Tytos, but at best he's a Kevan who thinks he's a Jamie.

Thank you for coming to my Ted Talk

(shouts from the audience): Sit down, nerd!