In a shallow baking dish, toss the asparagus with the oil to coat well. Add the salt, and pepper and toss.
Place the asparagus on the grill in a single layer, and cook, turning, until marked and tender, about 12 to 15 minutes. Transfer to a platter, sprinkle with the lemon juice and drizzle with olive oil, to taste. Cover with aluminum foil and let sit for 5 minutes before serving.
Large asparagus can be placed directly on the grill; smaller ones may fall through during cooking. If cooking thin asparagus, use a grill basket.