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Chickpea patties, pita bread filled with spinach, olives, capsicum, cucumber, hummus, focaccia with roasted veggies, tuna and rice, grain salad (grains, capers, sultanas), homemade veggie chips. The list goes on. There are SO many lunch options without nuts, even without meat and dairy, it's just a matter of getting creative.
...and finding things that actually get eaten- our eldest is given 10 minutes to eat so anything like noodles or sushi or pita stuffed with salad is off the list- he doesn't have time to eat it with his five year old hand eye co-ordination! TBH he even finds cheese sliced up on a sandwich a challenge when eating on the run which is why scrolls work well for him.