Behind the scoreboard at AT&T Park in San Francisco, the Crazy Crab'z stand sells a fresh, light crab salad like this. Sunset Recipes dressed it up with avocado and parsley, then serve the salad in lettuce cups to make it finger-friendly.
In a medium bowl, stir together crab, mayonnaise, parsley, onion and sugar until well combined. Add salt and pepper to taste, then chill until ready to serve.
Arrange lettuce on a large platter. Place about 2 tablespoons crab mixture onto center of each leaf. Top each with a slice of avocado, about 1/8 teaspoon cocktail sauce, a lemon wedge, and salt and pepper to taste.
Make ahead: Prepare through step 1 and chill, covered, up to 1 day.