1. Whisk together first 6 ingredients (through black pepper). Toss celery root with buttermilk dressing; let stand 15 minutes.
2. Meanwhile, place lemon juice in a bowl. Trim tops and bottoms from apples. Cut apples crosswise into slices, removing seeds and core with a round cookie cutter or paring knife. Transfer apple to bowl with lemon juice, and toss to prevent apple from browning.
3. Starting with apple slices, alternately stack apple with the celery root mixture on each of 4 serving plates. Garnish with additional chives, and serve.