I saw a child standing in the hallway crying because he didn't have his lunch money says left it on the counter at home is it appropriate for me as a teacher to buy that child a lunch?
I agree with this. Discretion is important because kids will learn to become reliant on the teacher. I personally would reach out to the parents after the third time, just to set a definite number on the case.
I think this is a great solution. Something to add might be allowing the student to get a lunch and pay for it later without the student understand the situation fully.
This seems like a wonderful course of action making sure to contact the parent in a way that doesn't put them on edge is great.
I like how you keep food allergies in mind. It's very important to consider any kind of food allergies because you do not want to hurt the student.