The courts have consistently ruled that student's 4th amendments rights can be strictly curtailed.
Yes, as it relates to dangerous objects (firearms, knives, etc) or inappropriate material (i.e. porn). Show me how a home packed lunch counts as either of those.
On a separate path, sue for infringement of 10th Amendment rights. It doesn't talk about rights reserved only to the states, but also to the people. A well argued case that "the people" as a whole have a right to determine what food they eat, no matter how nutritious it is, would stop many of these power grabs in their tracks.