Preheat broiler. Split the lobster tails by cutting through the center of the hard top shells and meat. Spread the halves of the tails apart. Place lobster tails, meat side up, on the unheated rack of a broiler pan. Brush tails with melted butter.
Broil 4 inches from heat for 12-14 minutes or until lobster meat is opaque. Gently remove the lobster meat from the shell and set aside.
Toast the rye bread, and lay the pieces out on a work station to assemble the sandwiches.
Place about 1/4 cup of sauerkraut atop 4 slices of the toasted bread. Place the swiss cheese atop the sauerkraut.
Place the lobster meat atop the cheese. Drizzle the thousand island dressing atop the lobster meat, and then top with the remaining slices of bread.
Transfer the sandwiches to a baking sheet and put them back under the broiler, just until the cheese is melted and the sandwich is heated through.