In a medium bowl, combine the mayonnaise, chives, parsley, Old Bay seasoning, egg, lemon juice, and red pepper. Season to taste pepper (you shouldn't need salt because the Old Bay seasoning has salt). Gently fold in the breadcrumbs and crab, being careful not to break up the crab pieces.
Form into 4 patties that are about 3 inches wide and 1 1/2 inches tall. Place on a parchment linked baking sheet, wrap with plastic, and refrigerate for at least 30 minutes or up to 24 hours.
Meanwhile, prepare the sauce by combining all of the sauce ingredients in a small bowl. Cover and refrigerate for at least 30 minutes or up to 3 days.
Place the flour in a shallow dish and lightly dredge each crab cake in the flour. Heat the oil in a large skillet over medium-high heat. Gently place each cake in the skillet and fry until golden brown and crisp, 4 to 5 minutes per side. Serve immediately with lettuce and sauce.