I know we are sharing anecdata from walking up the hills both ways but I'll add my own. I went to the Peoria Illinois school district. You can look it up - it was one of the poorest, worst performing, most underprivileged school districts in the state (outside of south Chicago and East St. Louis). I was on the reduced lunch program (40 cents a meal). But even we had a pretty boring affair of canned peaches and vegetables with lima beans with our Salisbury steak.
Also, the application for reduced lunch was included with the registration for the school so uptake was pretty high. At the time the district was legally compelled to feed kids whether they paid or not, so they were incentivized to maximize the reimbursement from the federal government to defray the costs.
If we didn't have money, our "free lunch" was a peanut butter sandwich. The problem is (at least in elementary and junior high) you probably weren't sure if your parents even paid the school for lunches. So you would get to the end of the line, select your entre, apple, and milk, and then put in your pin, and the lunch lady will take your tray back, and hand you a peanut butter sandwich (no jelly).
Not sure what the free lunch is now days, but probably not peanut related.
Also, the application for reduced lunch was included with the registration for the school so uptake was pretty high. At the time the district was legally compelled to feed kids whether they paid or not, so they were incentivized to maximize the reimbursement from the federal government to defray the costs.