Use scissors to snip through the top of the shell (round hard side), cutting through part of the meat and stopping before the tail. Carefully pry open the shell wide enough so that you can separate the meat from the shell, but keep it attached at the tail. Lift the meat up and over the shell.
Combine all lemon garlic butter ingredients in a bowl, stirring to mix. Brush along lobster tails to coat.
Set the oven rack about 8 inches from the broiler flame. Turn the broiler on at high setting.
Broil the lobster tails until cooked through, about 10 minutes.
While waiting for the lobster tails to cook, combine and stir together the bread crumb mixture.
Remove the lobster tails from the oven and top with bread crumb mixture. Return the lobster tails to the oven to broil for another 1-2 minutes until crispy.
Serve immediately and optionally garnish with fresh dill and lemon slices.