The bar for free school lunches in America isn't "extreme poverty". You've responding to HideousKojima's characterization of the program as though it is accurate, but he's wrong and if you're actually familiar with the subject matter you should have recognized that he's wrong.
Most working class families qualify for free or reduced price lunches. If you're at or below 130% of the poverty line your kids get free lunch. At or below 185% of the poverty line gets kids a reduced price lunch. How many children a family has is part of this calculation; the poverty line is set higher for larger families. This program spends something like 5 billion dollars a year giving lunches to tens of millions of kids. It's not a niche thing few qualify for. There are many schools where virtually every student is in the program.
Furthermore, schools will not allow kids to skip lunch. They are given lunch whether or not they have money and the matter is settled with their parents later. The few times I tried to skip lunch in school it turned into huge dramas and food was given to me even though I had chosen to not eat it.