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From what I can gather BOLT #4 is applying similar methods, such as obscuring previous and future hops from intermediate nodes, to the TOR network for routing payments across the Lightning network.
If that statement is broadly correct does that mean deploying a Lightning node on the TOR network would not be very compelling? There may still be benefits for NAT traversal and other things? But for obfuscation/anonymity is the idea that the Onion Routing BOLT will be as effective as TOR?
The answer to your question is a clear NO, as two very different problems are being tackled but the onion routing in the TOR network and by the Onion Routing in BOLT 04.
The idea of the Tor network is to hide your IP address. If you run your lightning node on a tor onion you will have a tor address and not even your channel partners can know where your node stands. In particular if you receive money on that node no one can see who you are
The idea of Oninion Routing (with the help of the SPHINX paper) in BOLT 04 is that you as the payer of a network hide who is receiving the money. Also you hide that you are the sender (though every node can send back error messages to you). If you pay a person with these oninion payments and this person is NOT using TOR for their lightning node you will know who the payee is (at least you know the IP address and to some degree where the computer stands) Others on the way do not know this (only the channel partner knows that the payee is involved in the payment process but it is not clear that it is the receipient to the channel partner). If however the payee uses tor the situation like discribed above in 1.) takes place.
So in order to maximize your privacy you should run your lightning node on TOR even though the routing of payments is a source based Onionrouting similar to TOR.
