If you're sure dairy is not the problem, how about cheese and raw veg for lunch? You have some fantastic cheeses over there.
Olives and roasted red peppers.
Peanut butter with fruit.
Greek yogurt with a little granola and fruit.
Tabbouleh with some cheese or a small tin of salmon (or sardines if you like them)
A tin of stuffed grape leaves with some cheese or a greek yogurt.
Chickpea salad - tin of chickpeas, tin of artichoke hearts, a little olive oil, lemon juice, parsley, onion flakes, salt & pepper (and a little shredded cheddar if you like)
Butter bean salad - butter beans, a couple roasted red peppers, onion flakes, olive oil, vinegar, cumin, salt & pepper
White bean salad - white beans, tuna, lots of oregano, olive oil, lemon juice, onion flakes, salt & pepper
The yogurt is the only thing that you would have to keep cold til lunchtime.