This answer is an educated guess and not the response of a qualified historian.
In the Tudor period, children of the upper classes would not have had to pack a lunch and go to school. They would have been taught at home by tutors and governesses, and only what they needed to know for their station in life. They would have been served meals by servants and would not have been carrying packed lunches to school.
Peasant children and children of tradespeople did not go to school but worked on the land or at a trade for their families' well-being.
Education of the sort we know had not begun when the Tudor period ended.