Combine first 10 ingredients in a large bowl. Add lamb; stir just until combined. Divide mixture into 10 equal portions, shaping each into a 1/4-inch-thick oval patty. Place patties on a broiler pan coated with cooking spray. Broil 2 minutes on each side or until done.
Combine cheese and yogurt in a small bowl; set aside.
Arrange 1 patty, 2 cucumber slices, 1 lettuce leaf, and 1 tomato slice in each pita half. Drizzle each pita half with about 1 1/2 teaspoons cheese mixture. Serve immediately.