@nathanael You need to provide an address to physically get the pizza, or you need to go in person to the restaurant. Also, the bank knows how much money you have, and what you bought, but it is private enough for most people (as the bank would be held liable if they shared your information without your consent or a judicial order).
I do not know anything about lightning or liquid, as I do not use cryptocurrencies and have no interest on using them.
@nathanael Though, I do have a question about your claim of nobody knowing your bitcoin balance:
If only you know your balance, how can it be verified that you are not lying about your balance when you buy something? How can you be prevented from printing money (bitcoin)?