Preheat the oven to 375°F. Crimp the edges of a 6˝ square of foil to form a loose pouch. Place the garlic in the pouch and drizzle with 2 teaspoons of the olive oil. Bake for about 30 minutes, until softened. Let cool for 10 minutes; peel the cloves.
Meanwhile, bring a large saucepan of salted water to a boil. Plunge the lobster in head first, cover and cook for 5 minutes. Using tongs, transfer the lobster to a bowl of cold water and let stand for 2 minutes. Shell the lobster and discard the vein that runs down the tail. Cut the tail and claw meat into ¾˝ chunks and put in a bowl. (The lobster can be refrigerated, covered, for up to 6 hours. Let the garlic stand at room temperature.)
Put the potatoes in a medium saucepan; add water to cover and 1 teaspoon of salt. Bring to a boil over moderately high heat. Lower the heat and simmer until tender, about 20 minutes. Drain. Pass the potatoes and roasted garlic through a food mill or mash them with a potato masher. Beat in the butter, heavy cream, ¾ teaspoon salt and ¼ teaspoon pepper; keep warm.
In a medium nonreactive skillet, bring the orange, lemon and lime juices, tarragon, minced chives and the remaining 2 tablespoons of oil to a boil over high heat. Add the lobster and stir until warmed through, about 2 minutes. Season with salt and pepper and stir in the coriander.
To serve, divide the mashed potatoes among 4 parfait or stemmed glasses. Spoon one-quarter of the lobster and citrus sauce into each glass and garnish each serving with 2 chives.