While a company can have teachers “eat lunch” with students as part of their working hours, they do not have the legal right to dictate what they eat.
As eating with students is legally considered to be “working time”, they must provide teachers with a legal rest break of at least 45 minutes.
Again, neither the company or school has a legal right to dictate what employees eat.
You are free to bring your own bento, free to leave the school and eat at a restaurant, free to buy something at the convenience store and eat it in the teachers’ room, and so on, if you wish.
Under the law, the company must provide an area for you to be able to eat – and that means an area where you can eat what you choose!