Bring a large saucepan of water to a boil. Plunge the lobster into the boiling water head first and cook until bright red all over, about 6 minutes. Transfer the lobster to a large rimmed baking sheet and let cool. Twist the tail from the lobster body and break off the claws. With scissors, cut down the tail shell and remove the meat. Cut down the center of the tail and remove the dark intestinal vein. Crack the claws and knuckles and remove the meat. Coarsely chop the lobster meat and refrigerate.
In a small saucepan of boiling water, blanch the basil for 30 seconds. Drain and rinse under cold running water. Squeeze the excess water from the basil and transfer the basil to a blender. Add the mayonnaise and puree. Transfer to a bowl and season with salt and pepper. Refrigerate the basil mayonnaise until lightly chilled.
In a large bowl, whisk together the flour, baking powder, baking soda and 1/2 teaspoon of salt. In a small bowl, whisk the buttermilk with the egg yolk. Make a well in the center of the dry ingredients and add the buttermilk mixture. Stir lightly, then fold in the lobster, corn, chives and melted butter. In a medium bowl, whisk the egg white to soft peaks and fold it into the batter.
Preheat the oven to 350°. In a large saucepan, heat 1 1/2 inches of oil to 325°. Drop four to five 2-tablespoon-size dollops of batter into the hot oil and fry, turning once, until golden brown, about 2 minutes. With a slotted spoon, transfer the fritters to paper towels to drain; season with salt. Transfer the fritters to a baking sheet and keep warm in the oven while you fry the rest. Serve right away, with the basil mayonnaise and lemon wedges.