Whisk flour, salt, black pepper, and cayenne pepper in a bowl. Gently press perch fillets into flour mixture to coat, shaking off any excess flour.
Heat butter in a skillet over medium heat until butter is foaming and nut-brown in color. Working in batches, place filets in skillet and cook until light golden, about 2 minutes per side. Transfer cooked fillets to a plate, squeeze lemon juice over the top, and serve.