For old and closed channels make sense to have a deleting data process. This helps also the performance of the node.

But for active online channels will be a challenge.

Apparently this is being worked on  https://github.com/Roasbeef/lnd/blob/017299fe6f3aec3d8c7ece84c383a47da59862f0/docs/forwarding_history_privacy.md

nout

Useless anyways. You must prove it was mine.

DarthCoin

You could, but if your peers don't delete logs and they keep the same nodes with logs on Amazon servers, then your payments are also retrievable.

Yes, they may think that it's payments to many people (not just single person), but it's still retrievable many years later and so it may connect to you in some other way (timing analysis, etc). I think lnd should default to autodeleting logs, e.g. after 30 days or whatever.

bitcoinplusplus

Peter Todd - Lightning's (Other) Toxic Waste Problem

btcpp

You could, but if your peers don't delete logs and they keep the same nodes with logs on Amazon servers, then your payments are also retrievable. 
Yes, they may think that it's payments to many people (not just single person), but it's still retrievable many years later and so it may connect to you in some other way (timing analysis, etc). I think lnd should default to autodeleting logs, e.g. after 30 days or whatever.