It's not accurate to think of Ln as a separate token moving on top of BTC
It's better to think of it as a network that claims ownership of sats inside BTC multi-sig contracts
There's no way to claim ownership of a sat that doesn't exist.
ie you cant create supply from nothing
The best anyone can do claim the sats in the channel (multisig contract) from their counterparty and hope they can get away with it.
