A very interesting topic! I never even thought someone might set themselves the task of hiding the fact that the coins they withdrew from an exchange are still in their possession.
I usually use Lightning to deposit bitcoins to exchanges, not to withdraw from them. And in my four years of using it this way, I’ve gotten the impression that none of the exchanges try to trace the network to figure out where a deposit came from. That’s why I think that after a withdrawal through Lightning, the exchange won’t try to find out whether the bitcoins remained with the client or were passed on to someone else.
You are confusing the adversary here. The exchange is not the adversary. As far as a well run business is concerned, an exchange would only do the minimum necessary to satisfy regulations relating to KYC/AML. This means that they would only do as much tracking as necessary, and not go beyond that. This could be something like simply cooperating with the data of Chainanalysis and government requests, they don't spend resources themselves to do extra than what is needed. Why would they? It costs more money, but they don't get anything in return. Actually, they even create losses by doing this.
The threat vector is the government, government and intelligence agencies. People casually forget that Bitcoin's data is permanent. Just because your information can't be traced now, that doesn't mean that someone won't be able to trace it in 5, 10, 15, 20 years.
But if I were paranoid, I’d probably solve the task like this: I would withdraw fiat money from the exchange into a bank account. From there, bank secrecy comes into play. Neither the exchange nor anyone who gains access to its logs would be able to know whether the money stayed in my bank account or was converted back into bitcoins on platforms like Robosats or LNP2PBOT, where there’s no KYC.
Bank secrecy is an outdated concept that no longer exists. Most banks are interlinked and most KYC data is interlinked. What one bank knows, the others can know too. What any bank knows about you, the government definitely know about it. I guess this part also stems from your confusion regarding the adversary. Exchanges come and go, they are just small cogs in a machine and are not important or dangerous.