Peel and wash the potatoes and cook them in boiling salted water for 20 minutes. Rinse trout and dab dry with kitchen paper. Sprinkle trout with approx. 3 tablespoons of lemon juice, season with salt and turn in flour.
Tap off excess flour well. Clean the salad, wash and pat dry. Wash, clean and halve the tomatoes. Season vinegar with salt, sugar and pepper, gradually add olive oil.
Heat the oil in a pan. Fry 2 trout one after the other on both sides for about 5 minutes. Place the fish on a baking tray lined with baking paper. Bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for approx. 10 minutes.
Wash parsley, dab dry and chop finely except for a few leaves for garnishing. Pour frying oil from the pan. Add about 6 tablespoons of lemon juice to the pan and bring to the boil. Stir in butter and parsley.
Season with salt and pepper. Drain the potatoes. Pour the vinaigrette over lettuce and tomatoes. Arrange lettuce, potatoes and trout on plates and pour the lemon butter sauce over them. Garnish with lemon slices and parsley leaves.