I can't find the free LN transaction on Muun even on their help/blog page what I only see is that the transaction fee of 6% to 20% is charged for LN transactions or 1 to 5 sats according to this Reddit post here
I can't even find any details about on-chain withdrawal fees for Muun so I guess their fees are also depends on Mempool status.
For me, if you want to receive a payout daily without a minimum or limit only ViaBTC(Already suggested above) is the best option where you can able to auto withdraw your earnings and transfer them to their Coinex exchange and if you are going to transfer it and withdraw to other exchanges they support other networks like withdrawing BTC from Coinex to Binance with BSC or TRC20 network it's cheap.