Deshell the lobster tails: Place each lobster tail, shell side down, on a cutting board. Cut down the middle using kitchen shears.
Spread the tail open so that there are two halves. Run your thumb between the shell and meat to separate them and remove the meat.
Cut the lobster meat into bite sized pieces. Place it into a bowl and pour buttermilk over it. Cover and chill for 30 minutes.
Heat 1/2 inch of oil in a large skillet over medium heat. Combine the flour and cornmeal in a separate bowl.
Dredge each piece of lobster in the cornmeal mixture and then drop into the hot oil. Fry until golden brown. Remove with a slotted spoon onto a paper towel-lined plate or wire rack.
Make the remoulade: Dice the pickles finely and combine with the remaining ingredients in a small bowl.
Assemble the sandwiches: Spread generous amounts of remoulade on both halves of bread. Place the lobster onto the bread, followed by shredded iceberg lettuce and dill pickles.