For some positions, I really enjoy doing lunch interviews. Nothing fancy, usually at Chili's, Applebee's, or some other chain restaurant with a name that ends in "eez". For manager positions, especially those with managers reporting to them, a lunch interview is an opportunity to see how a candidate interacts with other humans.
The lunch interview is not meant to torture, I promise. It is way, however, for me to gauge how you might treat employees at all levels. I am hoping that you will relax and just be yourself. Don't over think it. It's lunch, not brain surgery.
I am hoping to see the real you. Are you a gracious guest? Do you say please and thank you? Those are the easy ones. I spend more time observing how you treat the restaurant staff than I do observing how you interact with me. If you treat the hostess rudely or roll your eyes at the waitress when she walks away I can only assume that's how you treat your employees. If you don't make eye contact when talking to restaurant employees I find it difficult to believe you will be respectful to your employees.
By all means, don't try putting on an act, Chili's and Applebee's put a truth serum in all of their menu items. The real you will shine through.