Bitcoin banks that interoperate on the Lightning network are the most developed path to scaling Bitcoin for mass adoption. One problem faced by these banks is the implementation of fees for transactions that incur protocol fees on the Bitcoin and Lightning networks. This problem is particularly important in the context of providing both onchain and offchain liquidity, since different usage patterns can incur dramatically different protocol fees. We argue that the possibility of liquidity arbitrage on the Lightning network sets a market rate for inbound liquidity, and use an estimate of this market rate to develop new fee structures that properly price liquidity without overcharging everyday users. Furthermore, we perform simulations using historical transaction data from users of the Bitcoin Beach Wallet, and show that the new fee structures are able to account for different usage patterns under realistic conditions.