Rinse cleaned whole fish under cold running water. You can clean the fish yourself or ask the person at the seafood counter to do it for you.
Slice the lemons and garlic into thin pieces. Open the cavity of the fish and place the dill inside, then top with the lemon and garlic slices.
Close the cavity and tie with butcher's twine or place whole fish into a closed grill basket.
Place the grill basket on an outdoor grill over low heat or indirect heat. Cook until the flesh of the fish flakes away with a fork. Internal temperature should be at least 145 degrees.
Remove fish from grill and place on a sheet pan. Sprinkle the fish with sea salt and freshly ground black pepper.
Place under the broiler under constant supervision until the skin is crisped and browned.