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.