Question about school lunch

Hello everyone. So my daughter at kindergarten. School offering lunch for $0.40 cents per day( well it's not about money), I'm making her lunchbox at home. But all the time her lunchbox coming home almost full, she eats just tiny bit, maybe few bites of fruits and some cookies thats it(she is very picky eater and she likes eat outside). I'm thinking to pay for lunch at school, maybe that way she is gonna eat, maybe her lunch that I'm making is not fresh and hot that's why she is not eating. But not making her lunch at home, I will feel like a bad mom. What do u think? what will be good option?plz I need ur advice