Heat grill to medium. Place lobsters on the grill, cut side down, and cook until slightly charred and just cooked through. Remove meat and coarsely chop.
Whisk together lime juice, honey, horseradish, Worcestershire, hot sauce, tarragon, and olive oil in a medium bowl. Season with salt and pepper, to taste. Add the grilled lobster meat, avocado, and watercress. Serve in martini glasses and garnish with a lime wedge.