In a covered large skillet, cook asparagus in a small amount of boiling water for 3 minutes; drain. Meanwhile, for marinade: In a 2-quart rectangular baking dish, combine oil, lemon juice, salt, and the 1/4 teaspoon pepper. Add asparagus, stirring to coat. Cover and marinate at room temperature for 30 minutes. Drain asparagus, discarding marinade. Place asparagus on a grill tray or in a grill basket.
Arrange asparagus on a serving platter. Working over asparagus, use a cheese plane or vegetable peeler to cut thin, wide strips from the side of cheese block. Sprinkle asparagus with lemon peel and, if desired, additional pepper. Makes 6 servings.