Combine yogurt, lemon juice, and garlic in a medium bowl; season with salt and pepper. Set aside 1/2 cup of the yogurt mixture in a small bowl for serving. Stir cumin, coriander, turmeric, and allspice into remaining yogurt mixture.
Coat evenly all sides of chops with spiced yogurt mixture (avoiding the bone). Let chops sit at room temperature 30 minutes, or cover and chill up to 12 hours.
Preheat grill to medium-high heat. Wipe off excess marinade from lamb chops, discarding any remaining yogurt marinade. Grill to desired doneness, about 3-4 minutes per side for medium. Sprinkle the lamb chops with fresh parsley and serve with reserved yogurt mixture.
~ Free Tip ~ The chops may also be broiled in the oven about 5 minutes per side for medium or pan-seared in oil.