J.,
My kids are small, and we don't have eating issues. However I was a "thin" child growing up and my mom and I often got into fights about how much (or really how little) I ate. I will tell you this, no amount of fighting or nagging is going to help. When I wasn't hungry, I just wasn't.
I would encourage you to limit her "snacks" and other lunch food to healthy choices. When I had the choice, of course I would pick the chips, the lunchables, and overall, the sugar.
My mom took the approach, much later in my life, of ok, you don't want to eat, that's fine. But if and when I did want to eat it was milk, fruit, whole grains and protein.
I will also throw out there that I think some of the "picky eaters" are manipulating their parents with food. That said, I can certainly see how as a parent worrying about your child's health and nutrition can of course, be very disconcerting. What I'm suggesting is don't turn it into a fight. Don't let your child manipulate you. I have discussed this with our pediatrician, and she confirms, "Kids will eat when they are hungry and sleep when they are tired."
Try to take the stand of only healthy foods in the lunches. When your child comes home, don't give in JUST to get him/her to eat. Don't let them pick the snacks, or if you do, make sure that your house is only stocked with healthy options. Even my own children have "their days" when they don't seem to eat anything. The pediatrician said this is called camelling. Kids will eat and eat and eat and then it all gets backed up in their instestines. They feel "full". Once they have a BM, they will be in search of food again. Growth spurts - need food. Slow growth times - lack of food.
Be patient and trust yourself. Try not to worry. And try not to label your child (so s/he doesn't see himself as a "picky eater"...otherwise he may expect to be catered to with foods you know he'll eat.) Take a page from my mom's book. Don't give in. Just say, "OK, eat when you're hungry then." and don't bother with the sandwiches if they aren't being eaten. Give a cheese stix, fruit and crackers. If the school has questions, tell them your child is choosing/trying vegetarianism.
Best of luck. I really hope this passes. You're a great mom.