Steam the whole lobsters in a large, deep pot. Bring 2 inches of water to a boil and drop lobsters headfirst into the pot; cover, reduce heat to medium. Steam until shells are bright red, about 20 minutes, depending on the size of the lobster. Transfer to a tray and let cool. Remove meat from the lobster. Slice the tail meat ½ inch thick and slice claws in half. Cover and chill in fridge before serving.
Place the bacon slices in a cold, large skillet and cook over medium heat, turning occasionally, until crisp and browned, 10 to 12 minutes. Drain on a paper-towel-lined plate.
Slice tomatoes about ¼ inch thick. Arrange tomatoes, chilled lobster meat, bacon, sliced avocado, basil, lettuce leaves and brioche buns on a large platter. Place the chipotle lime mayo in a small bowl. Garnish with fresh chives.
For each sandwich, spread chipotle mayo on bun, then top with tomato, lobster meat, bacon, avocado, lettuce and basil leaf. Sprinkle with flaky sea salt.
Pair with a glass of local rosé and savor every bite.