What kinds of take aways should I expect from an informal meet and greet or lunch? Also, what should I be prepared to say?
It's difficult to say what, if anything, of professional importance will come from an informal meeting like this. You weren't given any specific instructions about preparing anything, so I don't think there's much to do in the way of preparing (other than making sure you shower that day :P)
Just try to keep your cool and not get lost in nerves. Be friendly, but remain professional. Let her set the topic of conversation and go with it. See what you see when its over.
The only word of caution I might give is to avoid complaining or bad-mouthing other employees if she starts asking for "your opinion about the company" or "any complaints" etc. Even if she's asking specifically for such things, getting into gossip and petty complaints with someone three levels above you might make you look spiteful or otherwise unprofessional. Also, if it's not the sort of thing a person in her position would need to address, then she's just going to send it back down the chain towards your direct manager anyway, which has the potential to start a game of broken telephone that could cause way more grief than it's worth.
I would recommend focusing on positive feedback and downplaying negative feedback in general. Otherwise, try to relax and have a nice, informal meet & greet.