and..... the rest? what happens when you don't "pass"? the child must go hungry?
If they find that a family can afford to feed their child, then no, they shouldn't get a free lunch. If they still aren't feeding their child when they can afford to, they are neglecting their child and the case should go to DCF.
Should we just give free lunch to anyone that claims they need it?
Allowing schools to come to their own independent decision on lunch eligibility based on spending is a horrible idea altogether. It's prone to abuse, since someone like Red Spy or INH could easily deny someone lunch eligibility if they bought an iphone as a gift for someone. It'd make sense for budget and numbers, but judging individual expenses can invoke bias.
I'd propose that they check your earnings, how much you spend on housing, added expenses and how much you save every year, and then come to the decision. Either way, not much will change. Unless you earn 80-100k a month but regardless live in a cardboard box to save more money, you're still going to save around 10-15 thousand dollars a year for savings
The school should ask for an income statement (with secondary proof such as a pay stub to ensure someone isnt lying) and use a generic set of percentages to estimate expenditure i.e. ~25% of income to housing, 5% to entertainment, 15% for food, etc.
If they find that you can't reasonably spare the $3 for a lunch, then you qualify. If they find that you have money but are just squandering it, then no, that application should be rejected.