You don’t have to answer questions, you could politely decline. It could be hard but you don’t have to disclose.

I wonder if there was a reason that she treated you and you accepted. Your birthday? Celebrating award you got? A date? Her thanking you for a favor you did to her? You are her guest from out of town? You two taking turns treating each other rather than splitting bills?

I can’t think of any other valid reason for friends to treat me for lunch. Especially if I don’t know that person for too long at all. How “new” is this friend?