Cut up vegetables or GF crackers with hummus (I forget which brand is labeled GF, but there is at least one)
GF tortilla chips (I know Green Mountain are labeled GF) and refried beans (if you use canned, choose the ones with just pinto/black beans & salt - usually they are labeled "No-fat refried beans" or "Vegetarian refried beans") with salsa (Pace is labeled GF)
Ham/salami (Hormel natural in the brown cardboard container is labeled GF) sandwiches on GF bread - I know that one is tough, literally! Or maybe the same ham/salami as a roll-up with corn tortillas or some sort of spread (is there non-dairy cream cheese? That would be a good base).
Corn tortilla burritos with toppings - endless possibilities there: beans, rice, meat, non-dairy cheese, salsa, lettuce, etc.
Leftover baked potato or sweet potato with whatever you normally put on them.
Chili with or without rice in a thermos
When I lived in Germany, one of the lunches at uni was warm rice pudding with fruit compote - you could make that or GF oatmeal with non-dairy milk & serve in a thermos.
Tuna salad with GF crackers - you could maybe make more of a vinaigrette dressing rather than mayo-based? The same could work for canned salmon.
Does your child like Indian food? I have a DD who is crazy about it & takes chickpea curry for lunch a lot, with or without rice. I make a big pot and keep it in the fridge. I vary the chickpeas with potatoes, sweet potatoes, cauliflower, etc.