Preheat the oven to 250*. In a heavy 10-to12-inch skillet, melt 2 Tblsp. of the butter over moderate heat. When the foam subsides, add the onion rings, a little salt and a few grindings of pepper. Stirring occasionally, cook the onion rings for about 10 minutes, or until they are light brown.
With a slotted spoon, transfer them to a heatproof plate, cover them loosely with foil and place in the preheated oven. Add 2 Tblsp. of butter to the skillet and drop in half of the apple rings. Cook them until they are golden on both sides, add them to the plate with the onions rings and cook the remaining apple slices similarly in another 2 Tblsp. of butter.
Keep the apples and onions warm in the oven while you cook the liver. Season the liver slices with salt and a few grindings of pepper. Dip the slices in flour, then vigorously shake off any excess. Add the remaining 2 Tblsp. of butter to the skillet and melt the butter over moderate heat.
When the foam subsides add the liver and cook it for 2 minutes on each side, or until the slices are light brown, turning them with kitchen tongs. Do not overcook. Remove the liver to a heated platter and scatter the apple and onion rings over it and serve at once.