Bimbo bread (a division of Freihoffer who also has many milk-free breads if you get the Family Grains) is dairy free. If you buy deli meat, do not get loaf meats as they often have milk in them. Do not get salami or pepperoni, as the curing process creates lactose. If she likes jam, just put a jam spread on her bread. Send her with fruits and veggies. Bagel bites with fruit. Tuna sandwiches. Nature Valley granola bars without chocolate. Bags of dry cereal.
If you're going to try an elimination diet, you have to go completely lactose free for a full month aka 4 weeks. It takes 2 weeks for the body to expel all traces of dairy from the body. It takes that long for the body to feel the way it should feel without dairy. Then the body needs to have 2 more weeks without dairy to see what it's like completely free of it. On the 5th week, you reintroduce dairy with a glass of milk to see how she reacts and you'll get a reaction within an hour or less.
Don't even give her lactose-safe products such as lactose-free milk in case she has a milk-protein allergy or sensitivity. Switch to soymilk or rice milk or almond milk. Find substitutes during that month that aren't just lactose-free but completely milk, cream, cheese, casein, whey, lactose, lactylate, milk-fat, butterfat, free. Check candies, cereal, drinks, potato chips, crackers, rice mixes, literally everything that comes in a box, bag or otherwise prepackaged. Anything that is a milk product of some kind, avoid it for 4 full weeks.
It's easier than it sounds.