Just twenty years ago paying in cash was still relatively normal. Nowadays in many countries cash has become a kind of curiosity. Most payments are processed by credit card for convenience. But there is one fundamental limitation of digital cash. While merchants can accept credit cards, private persons rarely can.
I in fact find it harder and harder to pay other people. I often do not have any cash. Then if I do I have cash the person I want to pay does not have change. I have many open payments that simply never get done. While credit cards have made paying in shops simple, they are slowly taking away the ability to make p2p payments.
For this we could of course use services such as paypal, but these do not have the same properties as direct p2p payments. And with lightning out, there is a simple and efficient solution ready to be used.
I think that as soon as the public perception of bitcoin recovers more and more people will start using lightning for small p2p payments. And this may be the first time people get into contact with bitcoin. Not as a speculator but as an actual user.
I nowadays always offer to pay anyone in lightning. Most decline, but I think numbers will keep growing.