Prepare the Lobster: Bring water to a boil, add some vinegar. Dispatch the lobster, then remove the head from the tail, trying to pull out the poop sack. Remove claws, feet, and dead man's fingers. Remove the antennas and scoop the insides of the head into a bowl.
Cook the Lobster: Blanch the lobster tail for 1-2 minutes, then place into ice water. Add the claws to boiling water next.
Extract Meat from Legs: Cut up the underside of the tail. Break apart the knuckles and use a rolling pin to squeeze all of the meat out of the legs.
Make the Sauce: Add some oil to a pan, add in all the shells, then remove them. Add shallots, tomato puree, and brandy, then flame. Add fish stock, thyme, and bay leaves. Pass off the stock, then add this to a pan with some butter, a squeeze of lemon, and all of the innards from the head. Hand blend in a pan.
Cook the Lobster Tail: Add the lobster tail to a pan, sprinkle around the bacon. Once colored on the bottom, flip over to color the top. Remove the tail.
Serve: Add a little bit of sea vegetables to your plate and place the cooked lobster tail on top. Pour the lobster head sauce over the lobster.