Are you certain she is only eating what you are giving her (besides the school lunches, which I agree can be HORRIBLE)? What grade is your daughter in? Are there vending machines at her school? Could she be sneaking foods when you aren't looking?
I only ask because I used to hit the vending machines at school and bring home all sorts of horrible junk in my backpack. I'd hide the junk in my room and my parents didn't have a clue.
My parents weren't strict about diet in our family. They encouraged healthy eating, but I think they raised us with a good balance of junk and healthy food. My problem was having undiagnosed ADD (not hyperactive, just inattentive, day dreaming, never quite focused on finishing anything.....), and because life can be so overwhelming for a young kid anyway, having undiagnosed ADD (I wasn't diagnosed until I was in my early 20's) can send a kid straight into comfort eating!
My point is, your daughter sounds like she has low self esteem and is probably suffering from what most young girls suffer from, which is having a completely unrealistic idea of what she thinks she should look like, which can lead to feeling depressed and hopeless, which leads to comfort eating.
I also imagine your daughter probably feels like she's getting a lot of pressure from you about what she is eating, which (please don't take offense to this) can actually make her feel so much worse about herself. I know your intentions are good, and you just want your daughter to be happy, because you love her, but be careful how you are approaching her about it. If she feels like you are unhappy with how she looks, it can send her into more comfort eating, but in private, when she knows you aren't looking (because she really doesn't want to disappoint you!). So that's one theory I have....
I also have another theory, which I only just thought of after reading your most recent post. If the above isn't the cause, and she's on board with eating healthy all the time, and isn't sneaking foods, AND you've had her thyroid checked (because I agree with the others, that can definitely be a culprit), then I'd start looking at what's in the "diet" foods she gets.
Take a look at the ingredients in what she is eating. I'm not certain, but I recall Special K bars and Nature Valley bars having something in them that made me quit buying them. Possibly high fructose corn syrup? Artificial colors? I don't recall, but I do know that they aren't natural. The best way to lose weight is to stick with foods that are made with natural ingredients. Cut out high fructose corn syrup and artificial colors and flavors. You do have to read labels. If you don't recognize an ingredient, don't buy the food. Last theory....
(and I'm sorry this is so long and scattered, I just keep having thoughts pop into my head as I go back and read your posts!
Is your daughter getting enough iron in her diet? You said you don't cook red meats, and I'm not sure what veggies she gets, so that's something you need to check. Low iron can lead to anemia, which can cause weight gain (and possibly thyroid problems, but I'm not certain about that...). Lean red meats are a great source of iron, so you might not want to cut them out of your diet completely. Have her iron levels checked! If she does need a supplement, get one from a natural foods store, to ensure that you're getting mostly iron in the supplement and not so much filler and artificial stuff! (same thing with vitamins in general!)
I don't know why, but I really feel for you and your daughter! I think it's probably because I battled so much with my weight growing up and I know how hard it can be! I hope something here can help.....