Pat fish fillets dry with paper towels to ensure a proper sear.
Season fillets with salt and pepper on both sides.
Lightly dredge fish in flour, shaking off excess to leave a thin coating.
Heat olive oil in a non-stick skillet over medium-high heat until shimmering.
Place fish in the skillet and sear for 3 to 4 minutes per side until the internal temperature reaches 145 degrees Fahrenheit and the flesh is opaque.
Remove fish from the skillet and set aside on a warm plate.
Reduce heat to low and add butter to the skillet, stirring until melted and foaming.
Whisk in lemon juice, lemon zest, and parsley to emulsify the sauce.
Spoon the lemon butter sauce over the fish and serve immediately.