There are always fees, but sometimes wallets hide them. Muun struggles with high network fees and passes those on to the user intermittently when making transactions, as opposed to Phoenix and Zeus that charge you only when you add liquidity to your channels.

You named two of the best already. Zeus, Phoenix, and also Mutiny if you’re holding Lightning sats. Ideally you should take some of them on-chain to put in cold storage once there’s enough to make it worth creating a UTXO.