You could sautee some mushrooms in a little butter or olive oil and add them to your pita. Or, you could maranate some beans (red, white, black, whatever you might have on hand) in a little balsamic vinegar and sugar overnight and use those. When eggs or cheese don't go with whatever it is I've made (but, honestly, when does cheese not?) beans or mushrooms are my go-to protein.
All that said, so long as you are getting the appropriate amount of protein for your age, weight, level of activity during the day, it doesn't much matter if you get it with every meal you eat during the day. If the pita you described above will fill you up for lunch, skip adding other protein, so long as you are getting it other ways.
Also, the reason meat is so popular as a source of protein is because it is a complete protein. Veggies and grains are incomplete proteins, but when combined properly, they become complete. A good rule of thumb is a dark, leafy green with a whole grain and beans or mushrooms make up a complete protein, and can be combined in many different combinations so you don't get bored.