Every time you spend either currency on a unit or upgrade, the price of a subsequent purchase goes up. This means that every time you spend Lanterns on an upgrade, you will have to spend the asking price plus one next time around. It's a similar story when it comes to money, but this “tax” is only incurred when buying multiples of the same unit. Be sure to diversify your investments!
Each turn you can also choose to purchase a Bribe for 5 lanterns (7 for the second and 9 the third) or choose charity instead, giving you 4 gold or 2 lanterns.