Toast the Walnuts: In a dry skillet over medium heat, toast the walnut halves for 3-5 minutes, stirring often, until fragrant. Remove from heat, let cool, and roughly chop.
Prepare the Apples: Core and cube the apples. Immediately place them in a large mixing bowl and toss with 1 tablespoon of fresh lemon juice to prevent browning.
Combine Salad Base: To the bowl with apples, add the sliced celery, halved grapes, and the cooled, chopped toasted walnuts.
Make the Dressing: In a separate small bowl, whisk together the mayonnaise, the remaining 1 tablespoon of lemon juice, sugar (if using), and a pinch of salt and white pepper until smooth.
Assemble the Salad: Pour the dressing over the apple mixture. Using a spatula, gently fold everything together until evenly coated.
Chill & Serve: For best flavor, let the salad rest in the refrigerator for 15-20 minutes. To serve, line a platter or plates with lettuce leaves and mound the Waldorf salad on top. Enjoy immediately for maximum crunch.