Think in terms of participants, not addresses. A participant in the lightning network has a couple of connections to various hubs, from which the participant is able to send or receive coin. The user is able to send coins to anyone connected to the lightning network by means of an atomic transaction through any path of the network. But the only payment from them that ever hits the chain is their settlement with the hub.
Imagine there was a TCP/IP data chain and corresponding lightning network. Everyone connected to the network has an "IP" channel with their ISP. Through this channel they can send data to anywhere on the network, and a traceroute shows what hops the data would take. But when settlement actually occurs all the network sees is the net amount of data that has gone through each segment -- without any context. There's no record preserved on-chain of who sent data to whom, just that X bytes went through the pipe on the way to somewhere unspecified.
So it is with lightning payment networks. You open a channel with a hub and through that channel send coins to anyone accessible to the network. Channels only close when a participant needs the funds for non-lightning reasons, or when hubs need to rebalance. And when they do, observers on the chain learn nothing more than how much net coin moved across that single link. They learn nothing about where that coin eventually ended up.