LN is a great interoperability layer even without cashu in the mix. There is really nothing preventing lightning to be cross chain or even totally trust-based on some edges of the payment. So as long as the shitcoiner finds a route to you, he pays in shitcoin and you receive Bitcoin.

I think, Calle is working on integrating Cashu in nostr clients and Cashu already supports LN payments and a Cashu balance could be in shitcoin.

Now the transition between shitcoin and Bitcoin happens at nodes that offer an exchange rate, so as your LN invoice might be 100sat, the sending node would search to pay as little shitcoin for that as possible but those nodes would earn a fee by enabling this interaction.