How do nodes communicate over Lightning network?
You are confusing two things here: payment channels and network communication. A payment channel is really the set of commitment transactions and their revocations. It is unrelated to network communications and the participants in a payment channel do not need to communicate via one specific way.

The network communications that nodes use to talk to each other (e.g. to update payment channel states) use TCP in a P2P manner. Like Bitcoin, a node establishes a TCP connection to other nodes, and those nodes have connections to other nodes. P2P is not a communication standard like TCP and UDP, rather it is a model of the network's structure and is a concept.