Heat gas grill to medium or prepare charcoal grill with medium-hot coals.
In a large bowl, add the ground lamb, yogurt, mint, Greek seasoning, lemon zest, garlic and salt. Stir until combined.
Form lamb mixture into 6 patties, 1 inch thick, about 7 ounces each. Cover and refrigerate while making yogurt sauce.
In a medium bowl, add the yogurt, feta cheese, garlic, lemon juice, salt and pepper. Stir until combined. Cover and refrigerate until ready to serve.
Grill burgers on the heated grill for 12 to 13 minutes, until internal temperature reaches 160°F on an instant-read thermometer, turning halfway through cooking time.
Cut 1-1/2 inches off top of pita bread. Insert a lamb burger, a few cucumber slices, tomato slice and lettuce leaf into each pita. Serve with yogurt sauce on the side.
Heat broiler. Coat broiler-pan rack with cooking spray. Place the lamb burgers on rack. Broil 4 inches from the heat, following directions in step 5.
