In a large sauce pan over medium heat, melt the butter and add the flour. Mix well with a whisk to prevent lumps from forming. Add the milk slowly and bring to a boil. Lower the heat and cook for about 5 minutes until the sauce thickens, but remains liquid. Add salt, pepper and nutmeg. Keep warm.
Prepare the Artichokes: (Skip this step if using canned or frozen artichokes.)
Fill a large bowl with cold water and squeeze in the lemon juice. Rinse the artichokes under cold water. Remove the tough outer leaves until the soft internal leaves are reached. Cut off the stem. Place the artichoke on its side and cut off the tops of the remaining leaves. Cut the artichokes in half, length-wise, use a sharp knife to remove the fuzzy choke, and cut each side into thin pieces – depending on size, this will result in 4-6 slices per half. Place the pieces in the lemon water to prevent discoloration.
Cook the Artichokes:
In a medium skillet over medium heat, saute the garlic in the olive oil. Add the artichokes and mix well so that they absorb the oil. Cook for 5 minutes, then add the wine, and salt and pepper to taste. Cook until the wine is absorbed. (Not that if you are using fresh artichokes, you will need to cook for an additional 15 minutes until they are tender. You may need to add some water along the way to prevent burning.) Set Aside.
Cook the pasta: Meanwhile, bring a large pot of salted water to a boil. Cook 2-3 pasta strips at a time for 1 minute each, removing them with a skimmer and laying on paper towel so they do not stick together. When all of the pasta is cooked, assemble the lasagna.
Assemble the lasagna:
Preheat the oven to 350 ° F.
In a 9×12 inch pan, spread 2 large spoonfuls of Béchamel evenly around the bottom. Place the first layer of lasagna, cover with a spoonful of béchamel, then add some artichokes and top with some mozzarella and sprinkle with Parmigiano. Ration the ingredients so that each layer is the same, except that the top layer should be only pasta with the remaining béchamel and a generous sprinkling of Parmigiano.
Bake for about 30 minutes, with the last 5 minutes on the top shelf under the broiler until golden brown.
Remove from the oven and allow to cool for 5 minutes before serving.