Included in the original Lightning Network specification is a proposal to use Onion routing for transactions. Onion routing, the same technology that powers the Tor network, would increase both security and privacy on the Lightning Network.
What this means for privacy
Currently, when sending transactions that cross multiple channels over the Lightning Network, each node in the chain knows everything about the transaction. Information such as who it came from, where it is going, and how much is being transferred is exposed. Having this information exposed is a privacy issue, as anyone can see who you are sending a transaction to. Onion routing intends to solve this issue. The content of the transaction is hidden to all but those involved when using Onion routing. Every other node in the chain simply knows enough to pass it along.
How Onion routing works
With Onion routing, each node is only told enough information to pass the transaction along to the next node on the route. This means that no-one can snoop on your transactions, but they will still get to their destination. Onion routing works by wrapping a packet (in this case a transaction) in more and more data. One piece of data for each node on the route. When passing through a node, the outermost data is decrypted and used to identify the next node. Before sending the packet, the node destroys the data that it used to figure out where the packet goes next and puts the data the next node will use in its place.
In the case of the Lightning Network, the node does the same process mentioned before but also collects its fee. The origin node calculates and adds each node’s fee during the creation of the transaction.