Using vegetable peel, peel carrot into ribbons. Toss with vinegar, salt and sugar. Let stand for 15 to 20 minutes or until lightly pickled.
Preheat broiler. To make koftas, thread lamb meatball mixture evenly onto 6 large metal or soaked bamboo skewers. Place on broiler rack; broil for 5 to 8 minutes or until golden brown and cooked through.
Remove koftas from skewers; serve in lettuce wraps with feta, pickled carrots, parsley and mint.
Alternatively, grill koftas on greased grill preheated to medium heat; pan-fry in large skillet or roast in 450°F (230°C) oven on lightly greased baking sheet for 8 to 10 minutes or until golden brown and cooked through.