Preheat your Grill at 375 degrees.
Split the lobster tails in half place then back side down.
Cut down through the center to the shell the whole length of each tail.
Pull the shell back, exposing the meat.
Pat the lobster tails with paper towel to dry.
Combine in a small mixing bowl the butter, lemon juice, dill, and salt until the salt has dissolved.
Brush the mixture onto the flesh side of each lobster tail.
Place the lobster tails onto the grill and cook for 5 to 7 minutes, turning them once during the cooking process. (The shells should turn a bright pink).
Remove the heat.
Serve with lime wedges!