No, you are missing the "network" part of "Lightning Network" it uses an onion-routing-like protocol to allow you to pay "through" other people.
So if I have a channel with you, and you have one with coinbase, I can buy bitcoin from coinbase through you without ever opening another channel, entirely counterparty-risk-free.
And in that scenario if you "refuse" to relay my transaction, or you try to do something sneeky like broadcast an old transaction that we made where I had .1 BTC and you had .9 BTC, that's breaking the agreement we have made and I can broadcast a counter-transaction to the blockchain proper which gives me all of the money in the channel (1 BTC).
And if I try to backstab you by broadcasting the "give me all the money" transaction when you haven't done anything wrong, you have a "counter-counter-transaction" you can broadcast that forces all the money in the channel to you (1 BTC). (and the counter-counter-transaction only works if you HAVE NOT broadcast the original transaction)
There is a bit more complexity to it, but that's the gist.
Easy peasy! Seriously, I've been skeptical of LN's success for its complexity. But reading your and others' comments here I can see that many people understand it clearly. It turns out I've been biased by my own ignorance. The more I learn about LN, the more hopeful I'm becoming. Thanks for helping.
Like most of bitcoin, it's a deceptively complex system made up of suprisingly simple parts.
I'm honestly still skeptical that LN will really take off (it needs the network effect to be useful), but the idea behind it is very elegant and solid.
If you're in the US, you might have heard of Starker exchanges (a.k.a. 1031 or like-kind). It's a method to defer realization of capital gains, usually on real estate. There are outfits that will help you form a multi-party exchange to match impedances between people who want to buy/sell properties, but some want to trade and some want to exchange for money.
Similar with organ donations. I might not match my wife's blood type, but I can donate a kidney to some other random person if there's a network that matches someone with my wife' blood type to her.
Counter-counter-transactions sound like textbook example of overengineering.
Bitcoin's only advantage at this point is its price, which will go away as soon as there is a crash. Then we can scrap Bitcoin, LN, and all the baggage and start with a clean 3rd generation crypto slate.
It's only overengineering if it is superfluous, and in this case it's not.
The counter-counter-transaction solves a very real problem and makes the entire system counterparty-risk-free. It's no more "overengineering" than your airbags are overengineering.
So if I have a channel with you, and you have one with coinbase, I can buy bitcoin from coinbase through you without ever opening another channel, entirely counterparty-risk-free.
And in that scenario if you "refuse" to relay my transaction, or you try to do something sneeky like broadcast an old transaction that we made where I had .1 BTC and you had .9 BTC, that's breaking the agreement we have made and I can broadcast a counter-transaction to the blockchain proper which gives me all of the money in the channel (1 BTC).
And if I try to backstab you by broadcasting the "give me all the money" transaction when you haven't done anything wrong, you have a "counter-counter-transaction" you can broadcast that forces all the money in the channel to you (1 BTC). (and the counter-counter-transaction only works if you HAVE NOT broadcast the original transaction)
There is a bit more complexity to it, but that's the gist.