Is this girl leading me on?

Hi Jak. Unfortunately I'm going to be cruel to be kind in my answer. As both a girl who has done this to a guy and a girl who has had this done to her by a guy, I would say walk away from the situation. Unfortunately many people go through phases in their life where they feel alone or unfulfilled and attention from a person who we know like us can help to make us feel better, even if we don't like the person as anything more than a friend. Knowing that a person is there to listen to us and support us is a great source of comfort. I truly believe that if a person wants to be with another person then all other issues and factors become irrelevant. If the girl liked you, she would say she couldn't make lunch BUT suggest an alternative date. Although she may not have been looking for a boyfriend, if she met you and really liked you she would change her mind because she wouldn't want to lose you. My advice is walk away. Hopefully she will realise what she has lost but you must be prepared for her not to follow.