Heat gas grill to medium-high or coals in a charcoal grill to medium-hot. Lightly coat grill rack with oil or cooking spray.
In a medium-size bowl, stir together yogurt, feta cheese, cucumber, salt and pepper. Cover and refrigerate until ready to serve.
Mix together lamb and Greek seasoning. Form into 6 equal-size patties, about 4 inches in diameter. Grill for 2 to 3 minutes per side or until internal temperature registers 160 degrees F on an instant-read thermometer.
Cut off top quarter of pita bread to form a pocket. Fill each with lettuce, tomato, onion, some of the yogurt sauce and a lamb burger. Serve remaining yogurt mixture on the side.