Yeah once you explore the nuance of how some of these exchanges integrate LN you learn some really interesting things. For example with Strike you can buy Bitcoin the normal way, but also if you just have cash in the account and scan a LN code, the recipient gets BTC but there is no purchase of BTC or conversion for the person who paid the money.

This means Strike is taking your money and moving BTC from their own private reserves rather than from their market maker. You didn't buy it, so technically that BTC is KYC free. All you did was send it to a wallet via a LN payment.

Now, Exchanges like Strike run their own LN nodes and probably are required to report those transactions, so the government would then need to get reported transactions off the node the BTC got sent to in order to determine the wallet that might be in custody of it. I don't know if they need both sides of that data, or just details from one of the LN nodes. This is most likely the reason they allow this, because there is a path to compliance.

From that point since its difficult to tell what wallet it comes from you send it on-chain to whirlpool or coinjoin.

I have some ideas how robosats can be used to do some fun things too. Personally I have not had a need for non-kyc BTC.

I honestly have no idea if any of that would work, but according to my understanding of things the theory is there.