Pick over the crabmeat for shells and cartilage. Put the crabmeat in a large bowl and add the parsley, bread crumbs, and lemon peel. Toss lightly. In a separate bowl or glass measuring cup, beat the egg and the egg yolk, using a wire whisk. Add the mayonnaise and beat until smooth. Add the horseradish, mustard, Worcestershire sauce, Tabasco, and pepper and beat until smooth.
Pour half the liquid over the crabmeat and toss lightly with a fork. Add the remaining liquid and toss lightly again. Gently pat the mixture into patties (about ⅓ cup each). Chill for 30 minutes.
In a heavy skillet, heat ¼ inch vegetable oil. When the oil is hot, fry the crab cakes over medium heat until golden brown on both sides, about 4 to 6 minutes per side. Drain on paper towels. Serve with Lily’s Tartar Sauce.