Remove the lettuce leaves and blanch them in boiling salted water for one minute. Carefully lift out and drain on a kitchen towel.
Remove the skin from the carrots, cut into wheels and sauté in butter. Douse with the soup. Soften the vegetables with the lid closed. Season to taste with salt and freshly ground pepper.
For the sauce, melt the butter. Add the flour and cook briefly, stirring until soft. Extinguish with the milk. Make the sauce on a low fire for about five minutes. Remove from the heat and stir in the cheese. Season the sauce with nutmeg, salt and freshly ground pepper.
Butter a baking dish. Layer 1/3 of the lettuce leaves. Spread half of the carrots evenly on top and drizzle with sauce. Cover with lettuce leaves. Add the rest of the carrots and a little bit of sauce. Finish with lettuce leaves and spread the remaining sauce evenly over the top.
Meanwhile, bake the lasagna in the oven heated to 200 °C on the second rack from the bottom for fifteen minutes.
In the meantime, melt the butter and briefly turn the breadcrumbs in it to the other side. After fifteen min of baking, spread this mixture evenly over the lettuce lasagna. Bake everything for another ten to fifteen minutes.