At first I thought he was being a bit critical...after all they made the effort to come to see him so he could buy lunch....but then I could see his point, they made the call and the plans they expected him to pay for it. I can see both sides so I wanted some other points of view on this.
I think all of this is irrelevant actually, because your family's established system is that they take turns paying when they come to see each other. It sounds like everyone involved - including your dad - understands and agrees with this system, since you've said that splitting the bill isn't an option, and neither is assuming the invitee always pays (since your dad doesn't reciprocate invitations). This means the only question is whether or not it actually was your dad's turn to pay. So, was it? Here's what you've told us:
-Cousin claimed that it was your dad's turn to pay.
-Dad never actually said that it wasn't.
-Dad's only rebuttal seems to be that Cousin just bought a new car and can therefore afford to buy him lunch.
-Cousin isn't normally the type to expect his elders to pay for him, and requesting that someone else cover the tab is unusual behavior.
So ehellions...who should have paid for the lunch? And wording to avoid a situation like this in the future?
Without more information, my best guess it that it sounds like it was in fact dad's turn to pay, and he just didn't want to because Cousin has money. Since the request is out of character for Cousin, I have to wonder if he may have picked up on some reluctance or resentment on your dad's end, and be pushing back a bit?
You did speculate that your aunt may have visited earlier with a different cousin and dad may have covered the bill that time. If that did happen it would most likely change my answer, but I'd need more info before I could factor it in.
For the future - is the issue that he resents taking turns, or that he honestly thought he had paid last time? My answer would depend on what his goal here is... whether he wants to change the system or just find a better way to keep track of it. Honestly I think he should tell them that taking turns is too complicated and confusing for him and he'd like to split the bill from now on, but you've already said that isn't an option.