Please read this guide
https://darthcoin.substack.com/p/lightning-wallets-comparison

DarthCoin

You don't have to turn them into sats. Your lightning wallet and on-chain wallet are the same. 

So after I deposit my on chain sats to Muun, I can use a Muun feature to turn them into sats which will make the fees cheaper?

Xclu

yes but you might get fucked on the fee via lightning with muun. They love to overcharge lightning tx fees. Better option is cctip/cwallet. Deposit to the btc address they give you, await confirmations, then you can swap instantly to 'sats' and send to any invoice. They do not support lnurl though.

Another option is fixedfloat. If you're in the US just use a vpn to spoof your location. They offer a swap from on chain to lightning for a small fee of 0.5% and minimums of only $1 usd.