No no no, that's just payment channels. Lightning is multi-hop payment protocol on top of the traditional channel idea. Alice has a channel with Bob, and Bob has a channel with the Pizza company, and the Pizza company has a channel with its employees for salary and tips. On delivery, Alice pays Bob, Bob pays the Pizza company, and the Pizza company keeps some and forwards on just Alice's tip to the delivery guy. This is coordinated and setup in less than a second of communication among the parties along the route (meaning Bob and the Pizza company need to have their nodes online; but there can be non-routable offline signers at the endpoints; the Lightning routing is an online protocol however), but the payment is atomic -- intermediaries like Bob only get their money if they forward it on (minus a reasonable micro-fee), and either all channel updates happen or none at all. It only takes about the same amount of time as a point of sale credit card transaction to setup and sign, and completion of the atomic signing step is finality of settlement, so long as the parties remain online to check for preemptive or fraudulent channel closure.
Lightning allows sub-second transactions with finality of settlement for any routable path along a peer-to-peer network of payment channels. Because of the six degrees of Kevin Bacon idea, anyone can pay anyone else on the network with a dozen or so different hops in the worst case, each hop taking a really small fee, like a hundredth of a percent. A true peer-to-peer electronic cash system, if you will.
As in this example, your long-lived channels as an individual are likely to be with your employer or payroll company, your mortgage company, your telco, your favorite restaurants, and other other regular payments you make or sources of income. As an organization your channels will probably be with your suppliers (accounts payable) and major customers (accounts receivable), as well as payroll and office supply companies, etc. But you're able to reach everyone on the network through these starting points. This allows you to do things like proactively "pull" in funds from accounts receivable to cover expenses, by routing through that part of the network. It maps pretty well onto both the individual and corporate use cases.
It also allows micropayment in bitcoin again.. the cost of a payment is basically the cost of maintaining these online routable nodes, and the message communication, which is probably sub-cents in the limit. It's possible you can, e.g., do a 5-cent payment per article view on a news website, or per song played on a future Spotify, etc.