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 is the muun on-chain more private? i mean it's hard to trace back to your own UTXO isn't it? I'm taking about path of Own Node --> Muun LN --> On-chain destination 
 Maybe its OK while fees are low. You'll have to look at your onchain footprint. I'm not sure its the best way to get a more private UTXO as muun isn't a real LN wallet. They use atomic swaps.

Sending into a LN wallet like Zeus or Electrum, then looping some out might be better.

There's also liquid (onchain-liquid-LN-onchain)

Or a simple custodial wallet like coinos.io or blink. Send onchain withdraw LN

Conjoins are another option 
 yeah man 🫂
i just wanted to on-chain gift a friend some sats then I realized it's not easy to do this without exposing my own UTXO. so i went thru the path of Muun by sending from my own LN node.
anyway conjoin is always a good idea, just it's relying on so many on-chain transfers that it's not perfect for the impatient. 
 OK, it might be good enough to hide your UTXO from your friend. But not for anyone doing onchain analysis 
 got it thanks🤙