For the dressing: In a small bowl, whisk together the mustard, salt, and several grinds of pepper and whisk in 1 tablespoon lemon juice. Whisk in the oil in a thin stream until the dressing is blended. (The dressing can be made 1 day ahead and refrigerated in an airtight container. I like to use a Mason jar for this. Whisk, or shake the jar, to blend the dressing before using.)
For the salad: Have a large bowl of ice water ready for crisping the vegetables. Using a sharp knife, a Japanese mandoline, or a food processor fitted with the slicing disk, cut the cabbage and radicchio crosswise into ribbons ¼ to ½ inch (6 to 12 mm) wide and place in the ice water. Using a vegetable peeler, remove the strings from the celery. Pluck off any leaves and add to the bowl. Shave the celery ribs into thin slices and add to the water.
Drain and dry the cabbage, radicchio, and celery. Place in a salad bowl. If the arugula leaves are large, cut them crosswise into ribbons and then add them to the bowl. (The salad can be made up to this point up to 1 day ahead, covered, and refrigerated.)
Up to 1 hour before serving, toss the salad with the dressing. Taste and add more salt, pepper, or lemon if needed. Just before serving, quarter and core the pears and cut lengthwise into thin slices. Add the pears and walnuts to the salad, toss, and top with the finishing salt.