Between not wanting to use the microwave, no refrigeration, healthy, and filling you got me stumped.
My lunches:
Various sandwiches (ham, turkey, chicken salad): all need fridge.
Occasional lean pocket: fridge and microwave
Leftovers from dinner: fridge, sometimes microwave
Soup in a thermos was all I could think of that meets all your requirements, but that was already mentioned. Maybe stop by the army surplus store and get some MRE’s.