Trim fat from lamb; cut lamb into 36 (1-inch) cubes. Combine lamb and next 10 ingredients (lamb through garlic) in a large heavy-duty zip-top plastic bag; seal bag, and marinate in refrigerator at least 8 hours.
Remove lamb from bag, reserving marinade. Thread 6 lamb cubes onto each of 6 (10-inch) skewers. Place skewers on a broiler pan coated with cooking spray, and broil 10 minutes, turning occasionally and basting with reserved marinade.
Fill each pita half with 6 lamb cubes, 1/4 cup lettuce, 1/4 cup tomato, 1 tablespoon onion, and 2 tablespoons Yogurt-Mint Sauce.