Prepare your grill grate. When coals are white, spread coals out for even heat distribution. Place the oysters directly on the grate with the deeper shell down. As soon as the shells pop open (about 5 to 8 minutes) the oysters are ready to eat. Serve immediately with the Lemon Dill Sauce.
Combine all the ingredients in a bowl and stir well. Refrigerate until chilled; the sauce will thicken as it chills.