1. Whisk together cider reduction, mayonnaise, honey, 3/4 tsp. salt, and 1/2 tsp. pepper in a small bowl until smooth.
2. Cut radicchio in half and cut out core. Set radicchio on its side and thinly slice lengthwise; transfer to a medium bowl. Put 2 tbsp. lemon juice in a small bowl. Cut apple in half lengthwise, core, and set flat on work surface. Cut into matchsticks, tossing them in bowl of lemon juice as you go.
3. Add apple and walnuts to radicchio and toss with dressing. Add more salt, pepper, and lemon juice if you like. Divide among salad plates and sprinkle with parsley.