Combine yogurt, lemon juice, and garlic in a medium bowl; season with salt and pepper. Set aside ½ cup of the yogurt mixture in a small bowl for serving. Stir cumin, coriander, turmeric, and allspice into the remaining yogurt mixture.
Coat all sides of chops evenly with spiced yogurt mixture (avoiding the bone). Let chops sit at room temperature for 30 minutes, or cover and chill for up to 12 hours.
Preheat grill to medium-high heat. Wipe off excess marinade from the meat, discarding any remaining yogurt marinade. Grill to desired doneness, about 3-4 minutes per side for medium.
Sprinkle with fresh parsley and serve with reserved yogurt mixture.
The chops may also be broiled in the oven for about 5 minutes per side for medium or pan-seared in oil.