Muun is a weird case. It’s not really a Lightning wallet.
Muun is non-custodial, you control the keys, but you don’t own the channel, when you send payment, Muun sends a lightning payment on your behalf while charging your on chain wallet for the payment through a submarine swaps.
This method can work in low fees environment, but when fees are high you’ll notive Muun charging quite a sizeable fee for each payment.