Cut tomato in half crosswise; gently squeeze out seed. Trim out and discard core; cut tomato into 1/2-inch cubes.
Mix tomato, mint, vinegar, and oil; spoon onto a platter or plates.
Trim excess fat off lamb. Barbecue chops on a grill over solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds). Cook, turning once, until lamb is browned and still pink in the center (cut to test), 7 to 9 minutes total. Set chops on tomato mixture.
Sprinkle meat with sunflower seed. Season with salt and pepper to taste.