How does it work for students from a low-income family who live in a district, or who attends a school, not covered by the scheme?
There is a daily fee for lunches that all students are charged at the end of the line when they collect lunch trays. These are usually a credit or ticket system where parents pay up front, and kids can get a set number of meals "on credit" if their account is empty. This may be something less appealing than the standard meal for the day that other children are served as a way to embarrass the family into paying.
Children can receive free or reduced price meals if they qualify based on family income and assets. They also check out in the normal way, with the meals showing as credit or getting tickets. When I was in middle school in the late 70s they made sure to give us different colored tickets so everyone would know who was poor. When the steel mill closed, we pretty much all got the free meal tickets.
The form to qualify is complicated and intrusive, making it difficult for parents to complete. it also counts assets. Factory closed but you had paid off the house? Sell it if you want your kids to eat.
In the US, Federal aid to schools is often based on "free or reduced price lunch" percentages at a specific building. The proposals under attack would essentially stop requiring individual families from having to document income and assets once a majority of students in a building qualify or by the percentage of families living at the Federal poverty level in the service area for that building. At that point, you can scrap the ticket/credit system and just hand every kid a meal.