The whole "The Lightning Network" idea falls in the same bucket as the "The Mempool" one.

For anyone reading and not understanding: there is no "the mempool". Each node has a different mempool.

Same with Lightning: any two lightning nodes are forming a network. There is one massive one that everyone and their mother plugs into because it's useful for their needs, but any pair of nodes can start a different network. There is an unknown number of private networks out there.