Not necessarily. My kids often eat tuna salad (turkey/chicken) wrapped in pita with lettuce and cheese. There are many alternatives to deli meat.
A sandwich isn't even a requirement anyways, sometimes my DD (12) will just take fruit, veges and ranch dressing, and a drink. That is what she wants. My son (16) likes to take in cold fried chicken left overs. And even cold spaghetti...eww. Great for me that he is the human left-over disposer. He eats me out of house and home, to be honest. My grocery bill will drop substantially when he goes to college.
Basically, if you don't mind eating it cold, it can be packed for lunch. Although, with little ones, you want things that can be easy to handle and easily wrapped.