Our daughter also has dairy/nuts allergies and eczema. She was able to bring home packed lunches at the previous state school, so her eczema was well under control. However, when she went to a private school, she had to eat school lunches as that was the school's (NGHS) and their Trust's (GDST) policy. The catering manager said he would cater for our daughter's allergies, but all he did was removed certain foods from set meals, without any replacements. So our daughter ended up eating substandard meals. Also, she was accidentally given butter on at least one occasion, and we found the school margarine contained butter milk. We suspected there was other food cross contamination as well.
Our daughter's eczema went from mild to severe within two terms, and still the HT refused to allow her to bring home packed lunched even when we presented her with a long letter from our GP. Many excused were given to us, but the real reason was probably because the school didn't want our daughter to set a precedence, and extra staff would be needed to supervise children not eating school lunches.
Our daughter now goes to a state school and she can bring home packed lunches again. Her eczema reduced rapidly and it's mild again. She is so much happier now, without painful sores and itchy eczema all over her body.
If your dn's food allergy is severe, then her parents much take full control of what she eats, with strict home packed lunches. Otherwise it's a real nightmare if her allergies ever get out of control.