Prepare the Louie dressing by whisking together mayonnaise, ketchup, lemon juice, Worcestershire sauce, hot sauce, and paprika in a medium bowl until smooth and well combined.
Check the crab meat carefully for any shell fragments and remove them.
In a large bowl, toss the shredded iceberg lettuce with about one-third of the prepared dressing until evenly coated.
Arrange the dressed lettuce on a serving platter or divide among individual plates.
Place the crab meat in the center of the lettuce.
Artfully arrange the tomatoes, cucumber, avocado, red onion, and sliced eggs around the crab meat.
Drizzle the remaining dressing over the salad or serve it on the side.
Season with salt and pepper to taste, and garnish with freshly chopped parsley.
Serve immediately or chill for up to 30 minutes before serving.