Muun wallet uses submarines swaps for their lightings txs, they don’t hold funds off-chain so they settle on the layer one, so their fees need to follow what is going on within the layer one.

“Muun Wallet Fees

Muun fees are determined by a mempool-based estimator, which prevents you from overpaying when unnecessary and underestimating the fee rate during high network congestion. Unlike other estimators that base their fee rates on past blocks, transactions, and fee rates, Muun’s fee estimator examines the current state of the mempool to suggest a next-block fee rate.”

https://h17n.com/mobile-wallets/muun/#:~:text=Muun%20co%2Dsigns%20daily%20transactions,home%20screen%2C%20as%20explained%20above.