In a large bowl, combine the egg, garlic, oregano, kosher salt and pepper. Crumble lamb and beef over mixture; mix well.
Pat into an ungreased 9-in. x 5-in. loaf pan. Bake, uncovered, at 350° for 60-70 minutes or until no pink remains and a meat thermometer reads 160°. Cool completely on a wire rack. Refrigerate for 1-2 hours.
For sauce, in a small bowl, combine the yogurt, cucumber, lemon juice, garlic, salt and pepper. Cover and refrigerate until serving.
Brush pita breads with 1 tablespoon oil; heat on a lightly greased griddle for 1 minute on each side. Keep warm. Cut meat loaf into very thin slices. In a large skillet, fry meat loaf in remaining oil in batches until crisp.
On each pita bread, layer the tomato, onion and meat loaf slices; top with some tzatziki sauce. Carefully fold pitas in half. Serve with remaining sauce. Yield: 8 servings.