I think some of you don't understand that Monero still leaves a trace on the blockchain, Lightning transactions leave no trace and are layered encrypted just like Tor routing.

There is a trace of opening and closing channels but in no case do they determine who you paid or who paid you. 

In combination with swaps or coinjoins for opening channels they give a really high privacy, although it is still not perfect. 

 Channel updates are public knowledge and you can be sure that there are many entities logging each and every change and building a searchable history, from which many correlations can be inferred.

Anyway, either one (ln/xmr) is much better than btc l1 when it comes to privacy and anonymity. 

 With private channels, amp and mmp you mitigate this type of attack.

Evidently the privacy in Lightning has its shortcomings, the biggest danger is the logs of the big LSPs if you are not routing the payment. 

 True. I haven't used LN much lately, is AMP/MPP a thing already or still soon™? 

 It has been implemented in Zeus for a long time.