If using live lobsters, steam or boil them. Let cool at room temperature. Use a cleaver to crack and remove the meat from the claws, knuckles and tails. Remove the cartilage from the claws and the intestine from the tails of the cooked meat. Cut the meat into 1/2 inch dice. You may pick all the meat from the carcass and freeze the carcass for soup or broth. Place the cucumber in a colander for at least 5 minutes to drain the excess liquid. Combine the lobster, cucumber and mayonnaise. If the salad is to be served within the hour, add the scallions. If not, add them 30 minutes before serving with salt if needed and pepper. Cover with plastic wrap and chill for at least 30 minutes before serving.;
Place a stainless steel mixing bowl on a damp cloth to keep the bowl from sliding around. Add the egg yolk, mustard and tarragon to the bowl and whisk until blended. Drizzle the oil into the bowl while whisking constantly. Be sure that the mixture is smooth and well blended at all times. Stop adding the oil periodically to allow yourself time to catch up; when there is no oil visible, continue adding and whisking. When half the oil is added, add 1 teaspoon of the lemon juice. Alternate between the remaining oil and lemon juice, whisking all the while, until both are incorporated. Whisk in the ice water. (The water stabilizes the mayonnaise, which prevents separating, a common flaw of homemade mayonnaise.) Season to taste with salt and pepper and cayenne. Whisk. Store in a small container, covered and refrigerated, until needed. To assemble the roll, prepare the lobster salad and chill for at least 30 minutes. Preheat a large heavy skillet over medium low heat. Lightly butter both sides of each bun. Place in the pan and cook for about 2 minutes until golden brown. Turn the buns over and toast the other side. Or toast the buns under a broiler instead. When they are ready, stuff them with the chilled lobster salad. Place each roll on a small paper or china plate. Garnish with pickles and potato chips. Serve at once.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.