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