Put the egg, lemon juice, water and mustard in a mixing bowl. Add 2 tablespoons of extra Virgin Olive Oil slowly while beating everything with a hand mixer until it begins to emulsify. Raise and lower the blender to mix in all the Spanish extra virgin olive oil. The result should be thick. Store it cold.
Cut the meat from the lobster tail and claws into 1cm (½ inch) cubes and put them in a bowl.
Add the mayonnaise, the Perrins sauce, the lemon juice, the hot sauce, the salt, the black pepper and the celery and mix well. Put in the refrigerator to marinate and cool for at least 1 hour.
Make a cut along the center line of the roll from top to bottom, not on the side, and without cutting all the way through. Cut off the edges of the hot dog rolls parallel to the central cut.
Heat 2 tablespoon of Spanish extra virgin olive oil over medium heat in a griddle or non-stick frying pan. Shake it to make sure the oil is covering the whole surface of the pan and add the hot dog rolls. Heat them and press them lightly with the fingers so that the roll is slowly browned and heated inside. Once golden remove the roll, add another tablespoon of Spanish extra virgin olive oil and repeat to toast the other side. Remove and open up the roll at the central cut.
Stuff the rolls with the marinated lobster and garnish with finely chopped chives on top.