There are several ways to make this vegetarian pasta dish ahead. 1. Prepare and refrigerate the components a day ahead and assemble and bake the lasagna about 2 hours before serving it. 2. Prepare, assemble and bake the dish a day ahead and reheat before serving. Several hours or day before serving, prepare Fresh Pasta: In large bowl or food processor fitted with chopping blade, combine 2 1/4 cups flour and the salt. In 1-cup measuring cup, beat eggs, 2 tablespoons water and the oil until well mixed; stir into flour mixture. Or, with food processor blade whirling, add egg mixture through the feed tube. Dough should form a ball. If it is too sticky, add more flour; if it is too dry, add more water. On lightly floured surface, knead dough a few minutes of until smooth. Wrap with plastic wrap; refrigerate one hour or over night. Prepare Mushroom Sauce: In small bowl, combine boiling water and porcini; set aside 20 minutes. In 6-quart saucepot, heat oil over medium heat. Add carrot, celery and onion; saute stirring constantly, until tender but not browned. Stir in chopped mushrooms, tomato puree, garlic and salt; heat to boiling over high heat, stirring constantly. Drain porcini, discarding liquid. Rinse porcini and add to mushroom-tomato mixture. Reduce heat to low and cook mixture 45 minutes stirring occasionally. Cool to room temperature and assemble lasagna or cover sauce and refrigerate over night. Prepare White Sauce: In heavy 2-quart saucepan melt butter over medium heat. Stir in flour, salt and nutmeg; cook until bubbly. Gradually stir in milk and heat to boiling, stirring constantly. Cool to room temperature and assemble lasagna or cover and refrigerate over night. About two hours before serving or the day before (if baking ahead and re-heating), in 6-quart saucepot heat 3" water to boiling. Divide pasta dough into 5 pieces. On lightly floured board roll out one dough piece to fit 3 1/2 quart (3" deep) glass baking dish. Add pasta sheet to boiling water being careful that it does not fold over. Boil 3 minutes. With 2 slotted spoons, transfer pasta to oiled colander on tray. Repeat with remaining 4 pieces, separating pasta sheets with pieces of aluminum foil that have been oiled on both sides. Heat oven to 375F. Assemble lasagna: Rub softened butter over bottom of baking dish. Top with 1/2 the mushroom sauce, 1 sheet pasta, 1/2 the white sauce, 1 sheet pasta, 1/2 the cheeses and 1 sheet pasta. Repeat ending with the cheeses. Bake 45 minutes or until the top is golden brown. Check after 30 minutes. If top is browning too quickly cover with foil. If baking a day ahead, cool lasagna completely, cover tightly and refrigerate. To reheat heat oven to 350F. Cover top of lasagna tightly with foil and bake 1 1/2 to 1 3/4 hours or until the center is hot. To serve, cut into 12 pasta-course or 8 main-dish servings.