Keep frozen cooked lobster in its sealed package, or place it in a leakproof zip-top bag. Submerge it in cold tap water for 15 to 20 minutes, turning the bag once halfway through
Empty the thawed meat into a colander and let it drain for 2 minutes.
Spread the meat over paper towels and press another towel lightly over the top. Removing excess water keeps the butter sauce rich and protects the buns from becoming soggy.
Slice large tail and knuckle pieces into chunks about 3/4 inch wide. Leave smaller claw pieces whole. Place the prepared meat in a dry bowl.
Melt 4 tablespoons of the butter in a small bowl or saucepan. Stir in the lemon juice, lemon zest, kosher salt, and black pepper.
Pour the lemon butter into a skillet set over low heat. Add the lobster and gently turn the pieces through the sauce for 2 to 3 minutes, stopping as soon as the meat is warm in the center. Do not allow the sauce to boil.
Melt the remaining 2 tablespoons of butter. Brush a thin layer over both outer sides of each bun.
Heat a clean skillet over medium-low heat for 2 minutes. Toast the buttered sides for 1 to 2 minutes per side, checking often, until evenly golden.
Divide the warm lobster into four equal portions so each roll receives about 4 ounces.
Spoon one portion of lobster into each toasted bun. Drizzle up to 1 teaspoon of the lemon butter from the skillet over each serving.
Sprinkle the rolls evenly with chopped chives.
Place a lemon wedge beside each roll and serve within 5 minutes while the lobster is warm and the buns are crisp.
