First of all, how did you find out about the lunch. Did she tell you? Because I am a woman and I want to point out that as a woman, if I have no intentions with a man, I make sure I pay for my meal at the least, and often his, because letting him pay feels like I'm insinuating I would date him. Where-as offering to pay seems far more just friendly. So, if you found out because she told you, and she payed so as not to give him any wrong impressions, your wife may well feel that she hasn't done anything wrong. I mean, at the end of days, part of loving our spouses was allowing them to love their lives. If you guys are walking on eggshells around each other, what kind of life is that?
My husband is close with many of his ex girlfriends, and is close friends with many many women. And at first it drove me crazy, but now I see that I could never replace those women, it would exhaust me, even if it was possible. And furthermore, he doesn't belong to me. We are partners, meant to enhance the quality of one another's existance. I'm the crown jewel, not the only one. And by thinking this way, it means that I don't have to needlessly alienate myself from my male friends. (Who support me emotionally, a great deal, and my hubby isn't jealous of them). It's may seem like a bizarre way of thinking, but old fashioned thoughts in this modern era, will ultimately hurt you far worse than learning to be accepting. The rule is, though, if she can do it, so can you! And if your wife turns out to be a hypocrite, well then you've got grounds for some talk of compromise. Certainly she shouldn't subject you to anything she wouldn't be willing to see done on your end.
I'll refer to my favorite line from a Bliss & Eso song 'True love is not a cage
It's a home in which you are free'
“Love is the ultimate outlaw. It just won't adhere to any rules. The most any of us can do is to sign on as its accomplice. Instead of vowing to honor and obey, maybe we should swear to aid and abet. That would mean that security is out of the question. The words "make" and "stay" become inappropriate. My love for you has no strings attached. I love you for free.”
― Tom Robbins, Still Life with Woodpecker