I would not use a client like that. But no one could stop them, even though LN network effects are already too big in nostr for others to succeed in adoption.
Discussion
The client wouldn't know it's a shitcoin if done right.
Clients currently request a LN invoice to pay. If it's an LN invoice it's LN, if the client requests something else I don't use it unless I'm missing something.
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.
Got it. If LN is the interop protocol it's fine, i don't care and will not even know what the other party holds as long as I get sats. The same applies to fiat, people use strike and cash app to send sats while they hold basically fiat.