In a medium bowl, combine the ketchup, prepared horseradish, Worcestershire sauce, fresh lemon juice, hot sauce, and garlic powder.
Whisk all the ingredients together until thoroughly combined and smooth. Ensure the horseradish is evenly distributed.
Taste the sauce and adjust seasonings as needed. If you prefer it tangier, add a touch more lemon juice. For more heat, add more hot sauce or horseradish. If it's too thick, you can thin it slightly with a teaspoon of water or white vinegar.
Transfer the cocktail sauce to an airtight container.