Combine flour, salt, and pepper in a small mixing bowl; mix well. Dredge crabs in flour mixture, shaking off excess flour.
Melt 1/4 cup butter in a large skillet over low heat; add oil, stirring well. Add dredged crabs, and sauté 5 minutes or until lightly browned, turning once. Remove crabs from skillet, and keep warm. Reserve butter mixture in skillet.
Add remaining butter to skillet, scraping bottom of pan to loosen sediment. Stir in parsley and lemon juice; cook over low heat until butter melts and sauce is thoroughly heated.
Arrange crabs on a serving platter; pour sauce over crabs, and serve immediately.