Preheat oven to 475°F. Line a large baking sheet with aluminum foil. If fillets are whole, cut in half along center seam.
Place flour in a shallow bowl. In a second shallow bowl, beat eggs and 2 Tbsp. water with a fork. Put cornmeal in a third shallow bowl. Season flour and cornmeal with salt and pepper, mixing each with a fork to combine. Arrange bowls in above order on a work surface.
Working with one fillet half at a time, roll fish in flour to coat. Shake off excess. Transfer to egg mixture and turn several times until thoroughly covered. Let excess drip off. Roll in cornmeal until coated.
Arrange fillets on baking sheet. Melt butter in a small saucepan over low heat and stir in lemon juice. Drizzle evenly over fillets. Bake until crisp on outside and firm to touch, about 10 minutes. Adjust oven temperature to broil and cook until golden, 2 to 3 minutes longer.
