Yes, money can be destroyed in lava in Terraria. When you drop an item of a white rarity in lava, it is instantly destroyed. Since many coins are a white rarity, they too will dissolve in the lava. However, there is a catch: the coin will have to be at least half-submerged in the lava for the lava to dissolve it.
Since lava flows downwards, once you find yourself close to lava, it is very easy to accidentally half-submerge your coins by mistake, so be careful.
Lava is not always a substance that works against you. You can also use lava as a crafting station, meaning you can craft items out of the lava to your benefit.
In conclusion, that answers if money can be destroyed/how it is destroyed in the lava in Terraria.