I work at my kids' school and also at lunch time in the cafeteria.
One thing, with some of the young children is: in the cafeteria... there is a LOT of kids. Each grade level, eats lunch at the same time. AND because of that, there is a lot of noise. The noise... really tweaks some of the kids. I know, they tell me. At my kids' school, there are cafeteria rules... and one of the rules is that the noise needs to be kept to a certain level. And we adults, enforce that.
Also at lunch time, some of the young kids/Kindergarten kids... this is the time... that they "miss" their parents or Mom. It is normal. So we comfort them and acknowledge them saying they miss Mommy... but then they need to eat and continue with their day. It is an adjustment. It is not only your, child.
The Teachers, cannot... sit with their class at lunch everyday. They use this time for their lunch break too, and/or to do work in their classroom. Or, IF a class has a Teacher's Aide, then they can help. But remember... if a Teacher's Aid is there to help assist.. that means that they cannot have a lunch break. The Teachers, that are in the cafeteria with their kids... are not eating. It is not their, lunch break. They are sitting with their class and working. So they forgo, their own lunch... to do this. At least, this is how it is, at my kids' school.
Kindergarten adjustment... can take, a couple of months.
My daughter when she was in Kinder, because she is sensory sensitive to "noise"... found the cafeteria very unpleasant. BUT she adjusted. I let her Teacher know. And I also would talk with my daughter about it. And she adjusted.
OR, if/when I see a Kindergarten child crying at lunch because of the noise or because there are so many kids there and it is distracting... I TELL the other table-mates "Hey kids, Sally here is feeling sad... can you all be nice classmates and help comfort her so she can feel happier?" And then I TELL the other table-mates... that this is NORMAL.... they all are young children, and we ALL miss our Mommy too. Its okay. But "lets all try and help each other okay? If you see someone sad, don't criticize, just try to be a nice friend..." and the kids, rise to it.
I feel for you, I know how you feel, and I also see kids like yours, who may feel this way at lunch. But so, as I mentioned, this is what I know per my kids' school, and how I handle it... being I work there.
Don't worry.
This is growing-pains for the child. And also for Mommy. It is a rite of passage.
Your daughter will be okay.