1. Shave carrots into thin strips using a vegetable peeler. Cut fennel and onion into very thin slices using a mandoline. Place carrots, fennel, and onion in a large bowl; add ice water to cover. Let stand 30 minutes.
2. Combine edamame, peas, 2 Tbsp. Lemon-Dill Vinaigrette, and salt and pepper to taste.
3. Pick crabmeat, removing any bits of shell. Gently toss crab with red bell pepper and lemon zest; season with salt and pepper to taste.
4. Drain carrot mixture well. Divide pea mixture among 12 small plates; top with carrot mixture, salad greens, and crabmeat mixture. Drizzle with remaining Lemon-Dill Vinaigrette just before serving.