Suggestion:

For DEX swaps, use Bitcoin, not LN. IMO this is the best practice. LN for micro payments is great, for DEXs... troubles are common (failed transactions, time outs, etc)

With Bitcoin low fees now, the opsec and robustness is appealing.

Yes, it will take 10 to 30 minutes to fully arrive to your Wallet, but you will get the notification that the transaction is on the way.

kycnot.me is a good source of links for DEXs that protect your privacy, just read the summaries for tge proposed DEXs, not all are the same, some are known for breaking the nonkyc policy