Who pays the miner fees for the closing transaction of a payment channel?
According to the BOLT 3 specification, the peer that funded the channel will incur the costs of closing fees. It also seems that these fees would be calculated before closing a payment channel. Both parties already have a transaction with a built in fee that can be used to close the channel that they can broadcast at anytime.

Reference: https://github.com/lightningnetwork/lightning-rfc/blob/master/03-transactions.md#closing-transaction