I don't know Bitcoin well enough to understand the LN paper, but I've read articles on the basic ideas and think I understand enough to implement LN on Ethereum, where it's much easier.

If channels were not networked together, then they'd only be good for recurring payments.

But there's a trick that lets you network them, so A can have recurring payments to B, and B can have recurring payments to C, D, and E, and now A can pay all the others via his one channel to B. And it's done in a way that prevents B from being able to run away with money intended for C,D,E.