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!
Lightning invoices contain only the payee's node public key. Their IP address can be looked up in any node's local map of the network as long as it was advertised in the "node_announcement" message. You can choose not to advertise your address at all, but you might as well set up Tor at this point.
Also, onion routing =/= Tor hidden service. When someone is paying you, they are not passing around your invoice. Instead, they construct an onion routing packet, which consists of multiple encrypted routing instructions that can be decrypted only by a specific hop. Each hop knows only about the next and the previous hop. That's what onion routing is.