Hello and welcome! I'm Sara, mommy to Cassidy (almost 4) and Joel (2), expecting #3 in March.
My daughter Cassidy is the opposite of shy, but she does have trouble controlling her attitude and expressing herself effectively. I have a couple of questions for you.
What kind of school are you referring to? Preschool?
I have a problem with the teacher taking away her lunch and snack time

Seriously. How is that helping? If Lilah's frustration was triggered by her inability to feel social with the other kids or to communicate, taking away two major times to practice socializing seems inappropriate.
Were you able to discuss with Lilah why she lost her cool? Perhaps if she has difficulty expressing herself, like my daughter, she felt that no one was listening to her, which only makes it worse. Especially if the teacher only punished her for the attitude. Every 4-year-old has a terrible attitude sometimes
Do Lilah's teachers understand her needs? As in, will they take the time to help her communicate? I've seen teachers on both ends of that spectrum: some take the time to really focus on the child and try to ascertain her needs, and some will just ignore the issue and try to sweep it under the carpet, so to speak. Sometimes the size of the class has a lot to do with this.
I hope you and Lilah can get this figured out soon! It's so hard for a child to feel like they don't fit in, or to feel inadequate with no way to express it