Melt butter in a large, heavy skillet over medium heat. Pour in lemon juice and swirl the skillet to mix melted butter and lemon juice.
Place salmon fillets, flesh side down, in the pan and cook until browned, about 3 minutes. Spoon lemon butter over the top of the fillets as they cook. Turn fillets over with a spatula and cook for an additional 1 or 2 minutes, depending on the thickness of the fillets. Season with salt and pepper.