Farmed abalone is available from select sources, but it's not commercially harvested. For this recipe, you can substitute shrimp: Finely chop 1 pound peeled and deveined shrimp in a food processor. Continue with the remaining procedure.
Place abalone in a food processor, and pulse until finely chopped. Transfer abalone to a bowl; add egg and next 5 ingredients. Stir in lime rind and next 7 ingredients. Combine citrus juices. Slowly add juice until mixture is slightly wet but still holds together. Cover and chill at least 1 hour.
Form chilled mixture into 10 balls (golf ball size); lightly roll in panko breadcrumbs. Flatten balls to form 1/2-inch-thick patties.
Pour oil into a cast-iron skillet to a depth of 1 inch; heat to 375º. Fry patties, in batches, 3 to 4 minutes on each side or until golden brown. Remove from pan, and drain on paper towels. Transfer to a baking sheet, and keep warm in a 200º oven. Repeat procedure with remaining patties. Serve with Dill Sauce.