An elevated take on the classic comfort dish.
Bring a stockpot of water to a boil. Add the lemons and enough salt to taste like seawater. Add the claws and tails; cook the claws for 5 minutes and the tails for 6 minutes. Immediately plunge into a bowl of ice water to cool. Remove the meat from the shells and chop. Set aside.
Chop up the heads and bodies of the lobsters with a cleaver.
Melt 3 tablespoons of the butter in a large pot. Add the heads and bodies; sweat to extract as much flavor as possible, 2 to 3 minutes. Add the large-diced carrots, onions and celery, the bay leaf and water to cover by 3 inches. Simmer for about an hour. Strain and add the liquid to a saucepan. Reduce for about 15 minutes to concentrate the flavor; you should have at least 6 cups.
In another pot, reduce the heavy cream and milk with half of the diced potatoes until the potatoes are cooked and the cream and milk have thickened, about 30 minutes.
Preheat the oven to 375ºF.
Melt the remaining 2 tablespoons butter in a clean pot over medium heat. Add the medium-diced carrots, onions and celery and the remaining half of the potatoes. Cook until softened, about 10 minutes. Grate truffle to taste into the sauteed vegetables. Add the chopped lobster meat and 5 to 6 cups of the reduced lobster stock. Slowly add the cream-potato mixture to taste, depending on how thick you want the pot pie. Fold in the peas and parsley. Season with salt and pepper and a touch nutmeg.
Ladle the lobster mixture into a 9-by-13-inch baking dish. Roll out the puff pastry large enough to fit the dish, if needed. Lay over the baking dish and brush the pastry with the egg wash. Bake until golden brown, about 35 minutes. Serve hot.