Heat a small, heavy skillet over medium heat. Add 1/2 cup oil; heat until oil is shimmering and oil bubbles around a shallot piece that's dropped into it. Add shallots to pan; slow-fry for 10 minutes or until browned and crispy, stirring occasionally. Remove shallots with a slotted spoon; drain on paper towels. Sprinkle shallots with 1/8 teaspoon salt.
Heat a large nonstick skillet over medium-high heat. Add remaining 2 tablespoons oil; swirl to coat. Add Brussels sprouts; toss gently to coat. Sprinkle with pepper and remaining 5/8 teaspoon salt; sauté 8 minutes or until lightly browned on edges. Reduce heat to low; cook 2 minutes or until tender. Stir in lemon juice; sprinkle with shallots.