Prepare Hard-Cooked eggs. Finely chopped the peeled eggs. Set aside.
In a medium mixing bowl, combine mayonnaise, onion, mustard, horseradish, lemon juice, salt, cayenne pepper and paprika. Gently fold in eggs and lobster. Season to taste.
Layer 4 slices of the brioche with lettuce and tomato slices. Spoon lobster egg salad on top of tomato slices. Top with remaining bread slices. Makes 4 main-dish servings.
Place 5 eggs in a single layer in a large saucepan (do not stack eggs). Add enough cold water to cover the eggs by 1 inch. Bring to a rapid boil over high heat (water will have large rapidly breaking bubbles). Remove from heat, cover, and let stand for 15 minutes; drain. Run cold water over the eggs or place them in ice water until cool enough to handle; drain. To peel a hard-cooked egg, gently tap it on the countertop. Roll the egg between the palms of your hands. Peel off eggshell, starting at the large end. Makes 5 hard-cooked eggs.