Well let's compare what both solutions do exactly:

- Monero creates big transactions with many senders and recipients (with some "fake addresses", i.e. existing addresses which in reality are not sending nor receiving anything mixed in afaik), and obfuscated amounts and receiver addresses. So while there are techniques which can identify senders if the user is careless, the exact transaction is very difficult to reconstruct.

- In Lightning, you would create a channel with the coins you want to "un-KYC", then transfer the coins via Lightning to another address, and close the channel (not mandatory). The intermediate process can't be followed on-chain, but in the case a chain analysis company operates a node and you happen to route through it, then it could detect you. Via onion routing this is prevented a bit but it's not perfect.

In my opinion, in both cases the privacy is not 100% perfect, but you're private if you do several transactions but spaced out a bit and using several addresses. The likelihood that someone is able to analyze your transaction pattern decreases with every transaction.

Lightning has however a slight disadvantage: if the channel is closed, then chain analysis companies will know that you used Lightning because of the script which is pushed on chain. And your counterparty in the channel will probably eventually close the channel if you stay unresponsive for a too long time. So then they could use this information to follow your way through Lightning if they operate Lightning nodes like explained above.

Another disadvantage is of course that you will pay more fees with Lightning in this case, because you can't simply re-use the channel to "un-KYC" other coins.

On the other hand, Monero is 1) less secure and 2) more volatile, so there are also some risks.

Some more info: https://www.voltage.cloud/blog/lightning-network-privacy-explainer