TO MAKE THE MEAT SAUCE: Put the dried mushrooms in a bowl and pour 1 cup boiling water over them. Let them sit for 30 minutes, then drain, reserving the water. Rinse the mushroom pieces thoroughly, chop them fine, and rinse again to remove all traces of grit. Line a sieve with a dampened paper towel and strain the mushroom-soaking liquid into a small bowl. Heat the olive oil in a large non-reactive skillet. Add the pancetta and onion and saute over low heat 5 minutes. Raise heat to medium, crumble in the ground beef, and add 1/4 teaspoon of salt and several grindings of fresh pepper. Saute 5 more minutes, stirring to break up the meat. Add the chopped chicken livers and the chopped porcini. In a measuring cup, combine 1/2 cup of the mushroom-soaking liquid and 1/2 cup hot water. Dissolve the tomato paste in this liquid and add it to the skillet. Bring to a simmer, cover the pan and cook 1 hour, stirring occasionally and regulating the heat to maintain a gentle simmer. TO MAKE THE SPINACH FILLING: If you are using fresh spinach, wash it carefully, and place it in a large pot with only the amount of water that clings to the leaves. Sprinkle lightly with salt, cover the pot and turn heat to high. As soon as the spinach wilts, reduce heat to medium and cook 5 minutes. (If using frozen spinach, cook according to package directions.) Drain the spinach in a colander, spray with cold water, squeeze out most of the water, and chop it fine. Put it into a bowl and add the ricotta, the egg, 1/4 teaspoon of salt and several gratings of fresh nutmeg. Stir all together well. COOKING THE LASAGNA: Bring a large pot of salted water to the boil. Fill a large bowl with ice water. Lay out several clean dish towels on a work surface. Drop the lasagna noodles a few at a time into the boiling water and cook 1 minute. Drain them with a slotted spoon, dip them into the bowl of ice water to stop the cooking, and lay them out on the dish towels while you cook the rest. ASSEMBLY AND BAKING: Preheat oven to 400F. Butter a 10-by-14-inch baking dish with 1/2 tablespoon butter. Cover the bottom of the dish with a layer of lasagna noodles. (Use about a quarter of them.) Spread 1/4 of the spinach-ricotta mixture over the surface. Sprinkle on 1/4 of the parmigiano, then 1/4 of the meat sauce. Make 3 more layers in the same way, ending with the cheese and meat sauce. Finally, dot the top with the remaining tablespoon of butter. Bake 15 minutes, or until the sauce is bubbling hot. Remove from the oven and let sit for 10 minutes before serving.