Preheat oven to 350 degrees F (175 degrees C). Line a shallow baking dish with foil.
Heat butter in a skillet over medium heat; pour in lemon juice. Cook and stir mushrooms until tender, about 5 minutes; stir in sherry. Place trout fillets with skin sides down into prepared baking dish; sprinkle with salt and cracked pepper. Pour the mushroom mixture over the fish.
Bake in the preheated oven until sauce reduces and fish flakes easily with a fork, about 30 minutes.