Edit: Here is an example of a lightning network enabled wallet that works as a lightning node itself. No payment processor needed: https://lightning-wallet.com
I think there is a fair amount of logistics to work out here. I may be wrong, and that would be great, but at the moment I'm not quite seeing how this is going to work in practice.
I'll be deeply surprised if lightning is ever used at the retail level by more than a couple shady internet casinos and John Galt themed vape stores.
Because you're both connected to a common lightning node, at least indirectly. There are several public lightning nodes that accept connections and they are joined together. Connect to one and you have access to their network.
> Similarly, if I want some random person to send me money, how do I convince them to run a lightning node and to let me connect to it?
Same as above. The lightning network is, of course, only going to work with other nodes who are also connected, but there is an incentive to join, since when you do, you can transact with all of its peers.
Jesus, this is precisely what the lightning network is for! Please, do a little research before dismissing it wholesale. The node you are connected to cannot refuse to pay, because you have a signed, but unpublished transaction of what he owes you (if he owes you). If he suddenly stops contact and says fuck you, you can just publish that transaction.
Seriously, this has always been the idea from the get go, so don't go blaming that you haven't read the latest update on how lightning works. If you don't understand something, don't go around spouting that it must not work.