Essentially the whole concept of LNURL is that the seller (e.g. the Restaurant) has to run a website (e.g. restaurant.com) that knows how to respond to a request with an LN invoice. 
So when you scan that static LNURL QR code with your mobile phone, the QR code just has the full link inside of it, e.g. restaurant.com/getinvoice/some_ID_123 and it returns "classic" LN invoice. 
Your mobile wallet know that when it reads QR code that has a link in it, it's supposed to make a request to the restaurant.com website to get invoice and pay it.  

It sounds great. As an only semi-technical person, I have a hard time following what's going on though (same for all of LNURL - it's hard to figure out). Wish there was some better documentation and intros. But maybe those are just meant as personal experiments.

gbks

I don't think so, in this case.  The point of sale app generates the invoice 100% offline.  Of course, the customer needs to get online to pay the invoice through the LN.  Also, the merchant needs to get online to spend the paid money.  But again, the point of sale app works offline (which is what the author intended).

Are we overloading the word "offline"? Surely the LN payment eventually needs to reach the online LN eventually?