Carefully wash the carp. Do not injure the outer skin. Bring a good 1/4 litre of vinegar to the boil. Place the carp on a plate (preferably the fat pan of the oven) and slowly pour hot vinegar over it until the carp skin turns blue.
Peel 1 onion and lard with bay leaves and cloves. Boil up the onion, pimento and peppercorns and about 2 1/2 litres of strongly salted water with remaining vinegar in a wide, flat pot (roaster with lid).
Cook the carp in the stock for 30-35 minutes. In the meantime wash apples, remove core. Cut apples into slices. Peel the remaining onions and cut them into slices as well. Heat 20 g fat in a pot.
Fry the onions in it until transparent, season with salt and lemon pepper. Add apples and steam briefly. Deglaze with cider and calvados. Steam for about 5 minutes, season again with salt and lemon pepper.
Heat lemon juice and zest. Add the rest of the butter and let it melt while stirring. Season sauce with salt and pepper. Remove the carp from the stock, drain a little and arrange each on some apple-onion vegetables on preheated plates.
Garnish with lemon slices and parsley. Serve with extra sauce. Boiled potatoes and creamed horseradish taste good with it.