In a small bowl, whisk together the lime peel, lime juice, garlic and sugar; whisk in the oil and season with salt and pepper. Place the steak in an 8-inch square baking dish and drizzle with 1/4 cup of the lime dressing. Turn to coat, then let marinate for 15 minutes.
Preheat the grill to medium-high. Season the steak with salt and pepper and grill for 6 minutes on each side for medium-rare. Let stand for 10 minutes, then thinly slice.
Meanwhile, in a large salad bowl, combine the remaining dressing and the onion. Add the steak, lettuce, carrots and mint; season with salt and pepper and toss.