Combine yogurt, 1 teaspoon lemon juice, dill, 1/4 teaspoon salt, and 1/8 teaspoon paprika in a bowl; cover and chill.
Sprinkle chicken with oregano, pepper, remaining 1/2 teaspoon salt, and 1/4 teaspoon paprika. Heat oil in a nonstick skillet over medium heat; add chicken, and cook 5 minutes on each side or until done. Transfer chicken to a plate; cover and keep warm. Add onion to pan and cook 7 minutes or until browned; stir frequently.
Cut chicken into 1/4-inch-thick slices and return to pan with onion. Sprinkle with 1 tablespoon lemon juice. Cook 2 to 3 minutes or until thoroughly heated.
Arrange lettuce and tomato evenly over pitas; top evenly with chicken mixture. Drizzle each with 2 tablespoons yogurt sauce. Sprinkle with 3 teaspoons feta cheese. Roll up.