Because of this
Are Lightning Network payments more anonymous than on-chain transactions?Yes, Lightning Network payments are more anonymous. They use
onion routing. In short, when a payment is being routed, an intermediary node knows only the previous and the next node in the path. It is impossible to tell who initiated the payment and what the final destination is.
You have to
explicity configure onion routing though, because the lightning nodes by default will use your public IP address as an identifier. That means, the Lightning invoice will also contain your IP address, so anybody who sees the invoice will know to which node its intended to!
Personally I think this default is a blunder, and I'd like to see software like c-lightning default to setting up a Tor hidden service instead.