Preheat oven to 200. Whisk together buttermilk, eggs, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a shallow dish; set aside. Whisk together cornmeal, flour, 1/4 teaspoon salt, and 1/4 teaspoon pepper in another shallow dish.
Working in batches if necessary, place crabs in egg mixture, and turn to coat. Let stand 5 minutes. Lift out, allowing excess to drip off. Transfer to cornmeal mixture; turn to coat. Tap off excess, and transfer to a rimmed baking sheet.
Heat oil in a large skillet over medium-high heat until hot but not smoking. Working in batches if necessary, add crabs; cook, flipping once, until crisp, golden brown, and cooked through, about 4 minutes per side. Using a slotted spatula, transfer crabs to a baking sheet lined with paper towels to drain. Place in oven to keep warm while making sauce.
Divide onion slices among plates; set aside. Pour off oil from the skillet; wipe clean. Add butter; melt over medium-low heat. Stir in lemon juice, chopped parsley, and 1/4 teaspoon salt. Drizzle onion slices generously with lemon sauce, and top with crabs. Pour remaining sauce over crabs. Serve with lemon wedges. Garnish with parsley sprigs.