Coat cold cooking grate of grill with cooking spray, and place on grill. Preheat grill to 350° to 400° (medium-high) heat. Snap off and discard tough ends of asparagus.
Place asparagus in a shallow dish; add oil and 1/4 tsp. salt, and toss well to coat. Grill asparagus 2 minutes on each side or until crisp-tender.
Add pepper and remaining salt. Squeeze juice from lemon over asparagus; sprinkle with cheese.