But a transaction to set up a channel needs to hit the chain first. What's the intended workflow for occasionally (once every few weeks) instantaneously ordering pizza via Lightning? Would I have to set up a very long lived channel with my preferred pizza place in advance?
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.
I brought this up with some ethereum devs at one point in a forum a year or two ago, and they addressed the questions pretty openly and graciously, but I still wonder about it. Essentially, they talked about the presumption of branches, subchains, etc. When that happens it seems the system would be a little more complicated than the classic crypto-libertarian currency model.
These chains get pretty large, and the overhead in terms of time and storage space seems well beyond what most people are used to now. Maybe people just have to get used to 15 minute payments, and having an extra drive or computer for financial transactions, as the cost of decentralized finance and economics, but from the current vantage point it seems burdensome to me, and only more so as adoption would grow.