Rinse cloud ears and lily buds under cool running water. Place in a small bowl, cover with cool water, and soak until soft, 15 to 20 minutes; drain. Pinch out and discard any hard spots from cloud ears, then rinse again; tear ears into 1/2-inch pieces. Remove and discard hard ends from lily buds; tie a knot in the center of each bud.
While cloud ears and lily buds are soaking, rinse and drain tofu; cut into 1/2-inch cubes. Rinse pork and pat dry; cut into 1/4-inch-thick matchstick-size pieces about 2 inches long. Rinse and drain bamboo shoots; cut lengthwise into 1/4-inch-wide strips.
In a 3- to 4-quart pan over high heat, bring broth and ginger to a boil; reduce heat, cover, and simmer to blend flavors, 20 to 25 minutes. Remove and discard ginger.
Stir in cloud ears, lily buds, tofu, pork, and bamboo shoots and bring to a boil over high heat. In a small bowl, mix cornstarch and vinegar until smooth; stir into boiling broth mixture and continue stirring until it boils again, 1 to 2 minutes.
In a small bowl, beat egg with a fork to blend. Remove soup from heat; immediately stir in egg, green onions, sugar, and pepper. Pour into a large bowl.