Sprinkle fish with salt and pepper. Dredge flesh side of 2 fillets in flour; dip in buttermilk. Dredge in panko mixture.
Melt 1 1/2 teaspoons butter in a large nonstick skillet over medium-high heat. Add 1 1/2 teaspoons oil. Add dredged fillets, crust-side down; cook 3 minutes on each side or until done. Remove from pan. Repeat procedure with remaining flour, buttermilk, panko mixture, fillets, butter, and oil. Top with parsley. Serve with lemon.