Use the oil to saute the chopped onion for a minute or two. Add the spinach and cook until it is heated through. Add a small pinch of red pepper flakes, a squeeze of lemon juice, and salt and pepper. Taste and adjust the flavors to your liking.
Add the cheese to the pan with the spinach. Taste again and add more cheese if you need to.
Cut the pita in half and carefully open each pocket. Put half of the spinach mixture in each half. Put the pita halves in a sandwich press and heat until toasty (2-3 minutes).