I'm with Japanfan on this. BaileyCatts said that she didn't know if it was a lunch interview, just wondered about the time. That gives her the option to say "I didn't realize we were going to lunch, so I ate before I arrived. Please do go ahead though, and I just have a cup of tea."
I think the chance that the person doesn't want to eat alone is one I'd take against the risk of trying to focus on an interview while eating and all the potential land mines that come with that.