In a small bowl cover mushrooms with warm water. Let soak for 30 minutes. Rinse well and squeeze to drain thoroughly. Thinly slice mushroom caps. Discard stems. Set sliced caps aside.
Meanwhile cut chicken into thin bite-size strips. In a medium bowl stir together green onions, lemon grass or lemon peel, salt, and pepper. Stir in chicken. Let stand for 15 minutes.
For sauce, in a small bowl stir together water, vinegar, and ginger. Set aside.
Pour cooking oil into a wok or large skillet. (Add more oil as necessary during cooking.) Preheat over medium-high heat. Stir-fry garlic in hot oil for 15 seconds. Add bok choy and onion; stir-fry for 2 to 3 minutes or until crisp-tender. Remove bok choy mixture from the wok.
Add half of the chicken mixture to the hot wok. Stir-fry for 2 to 3 minutes or until no pink remains. Remove chicken from the wok. Repeat with remaining chicken mixture. Return all chicken to the wok. Discard lemon grass, if used. Push chicken from the center of the wok.
Add sauce to the center of the wok. Cover and cook for 1 minute. Uncover wok. Add fish sauce, sugar, and mushrooms. Cook and stir for 2 minutes or until sauce is slightly reduced. Return bok choy mixture to the wok. Stir all ingredients together to coat with sauce. Cook and stir for 1 to 2 minutes more or until heated through. Serve immediately over hot cooked noodles. Sprinkle with red sweet pepper strips, if desired. Makes 4 to 5 servings.