In a large bowl of cold water soak lasagne squares until softened, about 15 minutes. In a small bowl toss together mozzarella and Parmesan.Spread enough red pepper tomato sauce in prepared dish to coat bottom.In a blender or food processor purée tomato pepper mixture in batches, transferring to a large saucepan as puréed, and stir in vinegar. Make wild mushroom mixture: In a small bowl soak porcini in the hot water 30 minutes and drain liquid through a sieve lined with a rinsed and squeezed paper towel into a measuring cup.Add sausage mixture to sauce and simmer, uncovered, 5 minutes. reserve 1/2 cup soaking liquid and chop porcini fine.
In a heavy saucepan melt butter over moderately low heat. Add milk and reserved soaking liquid in a stream, whisking, and bring to a boil, whisking.
Stir in porcini, nutmeg, and salt and pepper to taste and simmer over low heat, whisking occasionally, until thickened, about 5 minutes.