This salad uses just enough mayo to coat the shrimp, which will keep them moist but not drown them in a deluge of dressing.
Grate zest from lemons to equal 1 Tbsp. Cut lemons in half; squeeze juice from lemons into a measuring cup to equal 3 Tbsp.
Place each watermelon slice on a chilled plate. Season with desired amount of kosher salt and freshly ground pepper.
Microwave onion in a medium-size microwave-safe bowl at HIGH 25 seconds or just until onion is tender. Stir in mayonnaise, celery, 1 tsp. lemon zest, and 1 Tbsp. lemon juice. Stir in shrimp and tarragon. Season with salt and pepper to taste.
Place arugula in a medium bowl. Sprinkle with remaining 2 tsp. lemon zest and 2 Tbsp. lemon juice. Season with salt and pepper to taste; toss to coat. Arrange arugula mixture over watermelon; top with shrimp mixture. Serve immediately.