The Lightning Network is in many ways worse, rather than better, for privacy than on-chain Bitcoin transactions, simply because node holders have to at least know all of the route forward, and because of the forced address reuse.
Can you elaborate on why you think this is worse than having the whole network have a permanent history of a direct transaction between addresses?
Exactly. Plus address reuse doesn't really matter: if it ever becomes a security problem, they would rob satoshi's coins first.
I think you missed the onion routing part. The route is determined by the sender, forwarding nodes only know who they received from and who to forward to, as with TOR.