I would not go out for lunch with another man on my own... and if my sweetheart did that to me and I found out after the fact, i'd be in a World of self doubt, I would be upset and start wondering when the affair's going to begin.
The fact she did this without you knowing is a red flag in my humble opinion. Sure, if she had called first and said, "hey love, so and so wants to go eat lunch and i'm going to accompany him, want to join us?" that'd be different. But she did this stealth mode so of course your going to wonder, why.
and though many people will say things like, 'it's just a lunch' can't help it if your friend is the opposite gender. So uh, why the secrecy if it's no big deal right?
I'm jealous and protective by nature so i'm the wrong person to ask really. But no, In your shoes, I would not be a happy camper.