1Heat gas or charcoal 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.
2Place grill basket on grill over medium heat. Cook 15 minutes, shaking grill basket occasionally to turn and mix potatoes.
3Meanwhile, 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.
4Add asparagus to potatoes in grill basket. Cook about 10 minutes longer or until potatoes and asparagus are tender, shaking basket occasionally to turn and mix vegetables.