Preheat the stove to 225 °C.
Peel potatoes and celery, cut celery into pieces about the thickness of a potato and cut into slices 2 to 3 mm thick, like potatoes. Rinse apples, cut into halves or quarters depending on the size of the potatoes, remove seeds and cut unpeeled into 4 to 5 mm thick slices. After cutting, sprinkle the celery and apples with a small amount of lemon juice.
Grease a shallow ovenproof dish with butter and layer the slices of potatoes, apples and celery alternately, overlapping slightly. Sprinkle the apples and celery with the remaining juice of one lemon, sprinkle the nuts on top and season everything together with salt, pepper and cinnamon.
Stir the crème fraîche with the whipped cream, pour over the top and cook the gratin on the middle shelf of the hot oven for 40 to 45 minutes. It may color very slightly.