In the Wiki of Ice and Fire article for the Golden Tooth, it mentions that the “gold from the Golden Tooth helped establish House Lannister as one of the richest houses in Westeros,” which prompted me to think about the relationship the Lannisters have with their bannermen who also have gold mines. Do you think gold-rich bannermen like the Leffords and (formerly) Reynes have to pay an excise tax to House Lannister on the gold they extract? Was such a tax common historically?

The language about the Golden Tooth only appears in AGOT and disappears from all later books, and since the Golden Tooth is described at all points as a castle in a mountain pass as opposed to a mine, I think that’s out-of-date information. 

There are Westerlands Houses that have substantial gold mines – the former Reynes of Castamere, and whoever the overlords of Nunn’s Deep and the Pendric Hills are. 

As to whether they pay an excise tax, or just pay their feudal taxes in gold, I don’t know. In terms of a historical parallel, I happen to have found a perfect source for you, which explains that historically, monarchs claimed the rights to mining, which they then granted to others in return for mining taxes, although in England this was later changed to just refer to gold and silver mining.