In a 12-inch skillet, heat 3 tablespoons of the olive oil over medium heat. Arrange brussels sprouts in a single layer; cut side down. Drizzle with remaining olive oil and sprinkle generously with salt and pepper. Cover and cook for 3 minutes. Remove lid, and sprinkle sprouts with water. Cover and cook 2 minutes more. Sprouts should be just tender when pierced with a fork, and beginning to caramelize.
Remove cover and increase heat slightly. When cut sides are well-caramelized, shake pan, drizzle with lemon juice, and sprinkle with more salt and pepper to taste.