Fill a large pot with 2 quarts of water. Add half of the lemon (sliced), bay leaf, peppercorns, and salt. Bring to a boil.
Reduce heat to a simmer. Add the shrimp and cook for 2 to 3 minutes until opaque and pink.
Immediately transfer shrimp to an ice bath to stop the cooking process. Drain and pat dry once chilled.
In a small bowl, combine ketchup, horseradish, Worcestershire sauce, hot sauce, and the juice from the remaining lemon half. Whisk until smooth.
Chill both the shrimp and the sauce in the refrigerator for at least 30 minutes before serving.
Arrange shrimp on a platter or individual glasses and serve with the chilled cocktail sauce.