The show is not the books. The Lannister mines *in the books* are not empty. GRRM says the Lannister mines *in the books* are not empty.
The financial obligations of the Iron Throne and those of House Lannister are treated as entirely separate in the books. See this conversation between Tyrion and Tywin from A Storm of Swords:
"Extravagance has its uses. We must demonstrate the power and wealth of Casterly Rock for all the realm to see."
"Then perhaps Casterly Rock should pay."
"Why? I have seen Littlefinger’s accounts. Crown incomes are ten times higher than they were under Aerys."
"As are the crown’s expenses. Robert was as generous with his coin as he was with his cock. Littlefinger borrowed heavily. From you, amongst others. Yes, the incomes are considerable, but they are barely sufficient to cover the usury on Littlefinger’s loans. Will you forgive the throne’s debt to House Lannister?"
"Don’t be absurd."
The Iron Throne under Tommen is near bankruptcy; House Lannister is not. In The Princess and the Queen, when there was a national surplus, this is what was done with the royal treasury:
Ser Tyland Lannister was named master of coin in place of the late Lord Beesbury, and acted at once to seize the royal treasury. The crown’s gold was divided into four parts. One part was entrusted to the care of the Iron Bank of Braavos for safekeeping, another sent under strong guard to Casterly Rock, a third to Oldtown. The remaining wealth was to be used for bribes and gifts, and to hire sellswords if needed.
Casterly Rock and Oldtown served as the Fort Knox of Westeros. The problem at the end of ADWD is that the Crown doesn’t have the money to buy sellswords:
“Sellswords fight for coin,” declared Grand Maester Pycelle. “With enough gold, we might persuade the Golden Company to hand over Lord Connington and the pretender.”
“Aye, if we had gold,” Ser Harys Swyft said. “Alas, my lords, our vaults contain only rats and roaches. I have written again to the Myrish bankers. If they will agree to make good the crown’s debt to the Braavosi and extend us a new loan, mayhaps we will not have to raise the taxes. Elsewise—”
“The magisters of Pentos have been known to lend money as well,” said Ser Kevan. “Try them.” The Pentoshi were even less like to be of help than the Myrish money changers, but the effort must be made. Unless a new source of coin could be found, or the Iron Bank persuaded to relent, he would have no choice but to pay the crown’s debts with Lannister gold.
During his last small council session, Kevan worries that they will have to start using Lannister gold to pay the Crown’s debt. GRRM says the Lannisters still have money!!