Bring a large pot of salted water to a boil and add the live lobster. Lightly boil for 10 minutes. Drain and rinse with cool water until you can handle the lobster. Using a large knife, cut the lobster lengthwise. Remove all the guts and rinse again. You now have a cooked lobster that’s ready to eat as it is.
Pull out the tail flesh, and if you’re happy with the amount of meat here, you can work with the tail only. But if you have the will and patience, the meat inside the legs and antennae is also delicious.
Roughly chop the lobster meat into bite-size pieces and place in a bowl. This can now be chilled, or used immediately.
Stir in the mayonnaise, lemon juice, lemon zest, and diced celery. Season with salt and pepper to taste.
Heat up a skillet or grill pan, split open the buns (from the top if you can), butter them generously inside and out, and toast the buns on all sides until golden. A toaster oven works, too.
Scoop the lobster onto the toasted buns, sprinkle with the celery leaves, and optionally top with a few pieces of fresh Santa Barbara uni, then serve.