Break tough ends from asparagus; set aside.
Blend melted butter, olive oil, garlic pepper and lemon juice in a small bowl.
Place asparagus in a grill basket or in the center of a 12x12 inch sheet of heavy duty aluminum foil. Brush asparagus with half of butter mixture.
Place on grill. Grill covered 6-8 minutes or until asparagus is lightly charred and tender, carefully turning once.
Remove to serving platter. Drizzle with remaining butter mixture; toss to coat. Sprinkle with Parmesan cheese.