1. Clean the artichokes, cut them into pieces, and soak them in a bowl of water with the juice of 1/2 lemon. In a large quantity of boiling salted water, add the remaining lemon juice and the artichokes. Boil for 20 minutes, drain and press to remove excess water; pass through a vegetable mill, and put everything in a saucepan.
2. Pour a good amount of water into a pot, add the oil and salt; when the water starts to boil, cook the lasagnes. As soon as they are ready, remove them with a skimmer and place them on a clean kitchen towel.
3. Preheat the oven to 400°F.
4. In a saucepan, heat the artichoke puree; add the butter; sprinkle with sifted flour; cook for 5 minutes, over medium heat. Add the milk, mix gently. Continue cooking for 5 minutes. Season with salt, to taste, and sprinkle generously with nutmeg.
5. Butter a baking dish. Put a layer of lasagnes at the bottom. Cover with part of the artichoke cream, sprinkle with parmesan and continue to layer, until all the ingredients are used, ending with the artichoke cream and cheese.
6. Cook for 20 minutes, until the surface is golden brown. Remove from the oven and let rest for 5 minutes before serving.