In a large pot of boiling water, cook the lobsters until bright red all over, about 12 minutes. Let cool slightly under cold running water, then twist off the tails and claws. Crack the claws and remove the meat. Using kitchen scissors, slit the tail shells lengthwise, then remove the meat. Remove the dark intestinal veins and cut the tail meat crosswise into thin slices.

Half fill 2 large deep skillets with water and bring to a simmer. Crack 4 of the eggs into each skillet and poach over moderate heat just until set, about 3 minutes. Using a slotted spoon, remove the eggs from the skillets and pat dry with paper towels. Arrange the lobster meat on the toast. Top each serving with 2 eggs and keep warm.

Meanwhile, in a blender, briefly pulse the egg yolks to break them up. With the machine on, add the boiling water in a thin stream, then add the hot butter in a thin stream, stopping when you reach the milky liquid at the bottom; blend just until the butter is incorporated and the sauce is thick and pale. Add the lemon juice and cayenne. Spoon the hollandaise sauce onto the eggs and serve immediately.