Lightning can hop through payment channels, you can pay anyone on the rest of the Network, infinitely, sometimes for free (if someone wants lots of BTC going through their channel)
The clue is in the word "Network", if you can only pay one person again and again, it's not really a Network. Lightning is a network, where you can pay anyone.
Does lightning network can make transaction much faster and can it really lower the transaction fees. There are many claims that the lightning network can solve the slow confirmation and its name suggests that it has the power to do so. But it is too early to say those things we can only tell if we are already using lightning network. After which we can claim if it is fast or slow, if it is cheap or not.