Score both sides of steak in a diamond pattern by making shallow diagonal cuts at 1-inch intervals. Place steak in a resealable plastic bag set in a shallow dish. Set aside.

In a screw-top jar, combine salad dressing, lime peel, lime juice, and cilantro. Cover and shake well. Pour half of the salad dressing mixture into a small bowl; cover and chill until serving time. Add onion to remaining salad dressing mixture in jar. Cover and shake well; pour mixture over steak in bag. Seal bag; turn to coat steak. Marinate in the refrigerator for 24 hours, turning bag occasionally.

Drain beef, discarding marinade. Sprinkle with salt and pepper. Grill steak on the rack of an uncovered grill directly over medium coals for 17 to 21 minutes for medium doneness (160 degrees F), turning once. [Or place steak on the unheated rack of a broiler pan. Broil 3 to 4 inches from the heat for 15 to 18 minutes for medium doneness (160 degrees F), turning once.]

To serve, thinly slice beef across grain. Arrange salad greens, tomatoes, and, if desired, avocado on 4 salad plates. Top with beef. Drizzle reserved dressing over individual salads. Makes 4 servings.