Gather the ingredients.
In a large skillet over medium heat, melt 2 tablespoons of butter. Add the garlic and sauté until fragrant, about 30 seconds. Add the lobster and cook, tossing often until it turns opaque and is cooked through, 3 to 5 minutes.
Meanwhile, heat a grill pan or skillet over medium heat. Spread 1 tablespoon of butter lightly over the outside of the buns. Toast them in the pan on both sides until lightly browned. Set aside.
Transfer the lobster and garlic to a medium bowl. Melt the remaining 1 tablespoon of butter in the skillet.
Season the lobster with lemon juice, dill, chives, salt, and pepper. Add the freshly melted butter and toss until combined.
Place equal amounts of lobster mixture into each of the toasted buns. Serve with lemon wedges to squeeze over the sandwiches as desired.