Preheat a grill to medium.
In a shallow baking dish, toss the asparagus with the oil to coat well. Add the salt, and pepper, and toss to coat evenly.
Place the asparagus on the hot grill in a single layer, and cook, turning occasionally, until the spears are marked and tender, 12 to 15 minutes. Transfer the asparagus to a platter, sprinkle with the fresh lemon juice and minced garlic, and toss to combine. Cover the asparagus with aluminum foil and let sit for 5 minutes before serving.