Public schools already provide reduced cost or free lunches to qualified children.
At our private school, kids who lose or forget their lunch can get a "no-frills" lunch at the kitchen, which the parents are expected to pay back as soon as possible. That means they get a nutritious lunch but nothing fancy with no extras. Usually a sandwich, fruit, and milk.
When I used to sub terp at public schools, I was shocked to see how many free lunches were dumped into the garbage every day by the students. Their attitude was, "hey, it didn't cost me anything, so if I don't like it, I can toss it."