But on the other hand, there is no 'KYUTXO' because LN has no notion of UTXOs. Also I don't get how they want to handle Monero, since the transactions aren't public. Will they just ban it? Many open questions.
I don't think Bitcoin over Lightning Network will be looked at any different from first-layer Bitcoin. If a service provider accepts crypto payments, nothing changes. You will still be able to do your thing without KYC. If the coins get converted to fiat, third parties are required to request KYC, no matter what asset you use to pay. I hope exchanges will notice an outflux of users, but I remain skeptical. Centralized services will think of some new offers, give out some free coins or airdrops, and the majority will be happy to go along with it.