Combine 1 teaspoon lime juice and remaining rub ingredients; reserve remaining lime juice for Avocado-Mango Salad. Press rub evenly onto beef steaks. Place steaks on grill, turning occasionally.
For medium rare to medium doneness: Charcoal: Grill over medium, ash-covered coals, uncovered, 9 to 13 minutes. Gas: Grill over medium heat on preheated grill, covered, 9 to 14 minutes.
Meanwhile, prepare Avocado-Mango Salad. Combine mango, avocado and onion in medium bowl; sprinkle with cheese and drizzle with reserved lime juice, tossing gently to coat. Season with salt and black pepper, as desired.