Bring brussels sprouts, lemon juice, 1 1/2 teaspoons salt, and water to cover to a boil in a saucepan. Cover, reduce heat, and simmer 5 to 10 minutes or until tender. Drain and keep warm.
Melt 2 tablespoons butter in a large skillet over medium-high heat; add onion, and sauté 15 to 20 minutes or until caramel-colored. Add apple juice, and cook 2 minutes, stirring to loosen browned particles.
Add apple, garlic, and sugar; cook, stirring constantly, 5 to 6 minutes or until apple is tender. Add water chestnuts, next 4 ingredients, remaining 1/2 teaspoon salt, and remaining 2 tablespoons butter; cook, stirring constantly, 3 to 4 minutes. Gently toss in brussels sprouts.
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