Yes, I just tried it: this is what I did and it was all pretty seamless.
- I sent out a desired amount to my muun wallet using a LN invoice from my CASH wallet and it was received instantly for no fees.
- Once in my Muun wallet I sent it back to my CASH app bitcoin wallet using a Segwit address, as you cannot currently create a LN invoice within CASH.
So, it seems that while CASH supports LN it is only for withdraws and not deposits; this could possibly be added later as a feature by the CASH team, though. But as of now, only Segwit layer 1 address deposits are available to a CASH wallet.
Still, I paid ~7 cents with a 1sat/byte tx and it arrived in the next block since the mempool is clear using a segwit address.
If a retailer wants to take payments via BTC and LN they have two choices: use custodial wallets like Muun that support both Layer 1 and 2 protocols and move to a secure wallet where they hold the keys. Or invest in running their own nodes and a deploy a system that works for them.
I've been curious to try these things out for myself but I don't feel like I understand Muun wallet enough (as far as trusting myself not to screw it up)