Prepare the vinaigrette: Whisk together all vinaigrette ingredients in a medium bowl until combined.
Prepare the salad: Fill a large bowl halfway with water, and add lemon juice. Using a very sharp knife or mandoline, shave apple (skin on) into thin slices, discarding seeds and core, and place in bowl of lemon water. Repeat with turnips, daikon radish, and watermelon radish. (You will have about 4 cups apple, 3 cups turnips, 2 cups daikon radish, and 2 cups watermelon radish.) Drain and spread on a baking sheet lined with paper towels to dry.
Combine vegetable slices and 1/4 cup of the vinaigrette in a large bowl. Mix with hands to make sure to separate and coat all pieces. Stir in celery leaves and 1 1/2 cups of the walnuts.
Transfer to a serving platter; sprinkle with remaining 1/2 cup walnuts, and serve with remaining vinaigrette on the side.
The Walrus and the Carpenter, plus others, Seattle