Heat grill. In large shallow bowl, mix 1 tablespoon of the oil, 1/4 teaspoon of the salt and 1/4 teaspoon of the lemon-pepper seasoning. Add potatoes; toss to coat. Place in grill basket.
Place grill basket on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 15 minutes, shaking grill basket occasionally to turn and mix potatoes.
Meanwhile, place asparagus spears in same shallow bowl. Add remaining tablespoon oil, remaining 1/4 teaspoon salt and remaining 1/4 teaspoon lemon-pepper seasoning; toss to coat. Add asparagus to potatoes in grill basket. Cook about 10 minutes or until potatoes and asparagus are tender, shaking basket occasionally to turn and mix vegetables.