If it is just a friendly lunch, I'd keep it going. If she has a problem with something, she's the one that has to speak up about it. So I'd try it out at least once more and see how it goes. I'm not sure I understand if you're seeing her as a potential mate, though. Is she on the same page as yours? I think you need to clarify things with her right from the start, or there could be problems in the future. Sending many hugs to you