For the shrimp: In a medium pot filled with water squeeze the lemon and drop in along with the onion, salt, bay leaf, and peppercorns. Bring to a boil over high heat, simmer for 5 minutes to develop the flavors.
Reduce the heat to medium and add the shrimp. Gently cook until the shrimp turn pink and opaque. Strain, cool, and peel the shrimp. Refrigerate to chill through, about 30 minutes.
For the sauce: In a small pot combine the ketchup, horseradish, lemon juice, and hot sauce. Warm over medium low heat to develop the flavors, about 5 minutes. Chill in the refrigerator, about 30 minutes. Stir in the parsley just before serving.