Place the flour in a shallow bowl. Generously season the fish with salt and pepper. Lightly dredge both sides of the fish in the flour, shaking off the excess.
In a large skillet over medium-high heat, melt 4 tablespoons of the butter. In two batches as to not over-crowd the pan, cook the fish until golden brown on both sides and cooked through, about 3 minutes per side. Transfer the fish to a plate and tent with foil to keep warm.
For the sauce, add the remaining 4 tablespoons butter to the pan and cook over medium-high heat, stirring with a wooden spoon to scrape up the browned bits from the bottom, until the butter stops foaming and begins to brown, about 3 minutes. Reduce the heat to low and stir in the pecans and cook until warmed through, about 1 to 2 minutes. Add the lemon juice and season with salt and pepper to taste.
To serve, place a piece of fish on each plate and spoon the sauce over the top.
