Hi P.,
I am vegan so I can definitely suggest some non-dairy lunches. My son is sugar sensitive so I try to be creative without adding too much (if any) sugar. Also, I generally shop at Sunflower or Sprouts but some things can also be found at Fry's, Safeway, etc. - as long as they are closer to more "upscale" neighborhoods. Here are a few things I pack for my 5 year old vegetarian son:
Tofu salad sandwiches - similar to egg salad but I use Vegannaise (vegan mayo). I do not have exact measurements down but rather prepare to taste/eye. To prepare crumble extra-firm or firm tofu into a skillet with about 1 tablespoon of olive oil over med-high heat. It takes some time for the tofu to brown. In a food processor I put in the vegan mayo (depending on how creamy you like it - start with a tablespoon or so), one small-medium avocado, some yellow mustard, a pinch of sea salt, and some black pepper. I blend that up and put in fridge to cool. After the tofu is browned to your liking (generally not crispy but not too mush either - I prefer the consistency of WELL cooked scrambled eggs. I then put the tofu in a container and stick in fridge until cooled. Once both are same temperatures I will mix together adding diced sweet pickles. I have served this either on a sandwich bread or make mini sandwiches with crackers.
My son loves peanut butter! So he will have pb & j (no sugar added preserves), peanut butter and banana sandwiches, or peanut butter and cracker (Ritz type crackers) sandwiches. Another treat for him when he was a toddler was apple slices and a dish of peanut butter to dip them in. I do make cheese sandwiches for him on occasion - but am careful due to the fat content of vegan cheese substitutes.
Another favorite is a veggie dog (Smart Dogs are our faves) on a Snuggle (these are bread-like buns I found at Sprouts - and I think Fry's might also carry them). I keep ours in the freezer and the Smart Dogs in the fridge. I will make his lunch the night before - simply take the Snuggle out of the freezer, put the Smart Dog in it, and put it back in the fridge until morning. My son will add ketchup or mustard to it at school if he wishes. He eats them cold 95% of the time when home too - dunno why he prefers them this way - he just does! haha. (The same company that makes Smart Dogs - I think it is called LiteLife - also make vegan "meats" like bologna, turkey, and ham. I suggest these as you stated you were looking for healthy alternatives - and these alternatives are generally more healthy than the meats they mock.
He also loves bagels and (vegan) cream cheese and loves cold left over lasagna! (I make mine with medium to firm tofu for the ricotta, soy milk and flour for a "creamy" taste and add lots of veggies like mushrooms, zucchini, yellow squash, and eggplant.) But if your child is at a day care that will warm her food she might like it better.
In the summer time he likes fruit salad - just a bunch of fruit cut up in a dish.
I also make wraps (tortillas) for lunches or dinners. I use vegan cheese, veggies (lettuce, tomatoes, cucumbers, shredded carrots), avocado, vegan mayo, mustard, and some sort of protein i.e. Morning Star Farms Chik'n Strips, marinated & breaded tofu strips (pre-cooked), etc.
For additions to his lunches I will include vegan: crackers, yogurt, pudding, dried fruit, homemade granola bars, fresh fruit (bananas, apples, strawberries, blueberries, plumbs, peaches, etc.) and sometimes Annie's Bunnies (variety of flavors - have some sugar in them but no dairy).
I found it is difficult to make sure he has protein for every lunch so try to compensate with at home snacks and meals.
The stores I listed above have a good selection for non-dairy alternatives so you might be able to find alternatives for your regular recipes that call for dairy.
Anyhow, hope some of those ideas are helpful. Good luck! =)