Cut onions from top to bottom into thin slices. Cut tomatoes from top to bottom into thin slices. Put into two small bowls and set aside.
Combine oil, vinegar, salt, and pepper in a small bottle or bowl. Heat Pita bread in a preheated 350° F oven (about 10 minutes, until warm).
Fold each pita bread in half across the center. Fill each with some strips of cooked lamb or beef. Sprinkle with a little of the oil-vinegar mixture.
Top with some shredded lettuce, sliced onions and tomatoes, and oregano. Sprinkle again with oil-vinegar mixture. Serve at once.Servings: