Arrange the sliced potatoes and lemons in a layer at the bottom of a large greased shallow baking dish or roasting tin and dot generously with butter.
Place the fish on top of the potatoes. Season with salt and pepper and scatter the olives over the snapper.
Sprinkle the fish generously with olive oil and bake in a preheated oven, 190°C (375°F), Gas Mark 5, for 30-40 minutes, depending on the size of the fish, or until the flesh flakes easily and is tender. Serve at once, sprinkled with dill.