Heat 1/2 cup oil in a large saucepan over medium-high heat. Add onion and garlic and sauté for 3 minutes. Stir in the beef and sauté for 5 minutes or until well browned. Remove the beef with a slotted spoon and set aside. Add the sausage to the saucepan and sauté until browned. Return beef to saucepan.
Add the wine to the saucepan and cook for 5 minutes or until it has evaporated.
Stir in tomatoes, tomato paste, and water. Add salt and pepper. Simmer, stirring occasionally, for about 2 hours or until thick and rich in flavor. If needed, add more water, a quarter cup at a time. If sauce is fatty, either skim off the fat or put a few layers of paper towel on the top to absorb the excess fat. (If you have the time, refrigerate the sauce until the fat congeals on top; then simply lift it off.)
Put ricotta into a cheesecloth lined colander and allow it to drain in the refrigerator for about 2 hours. Combine with egg yolks; blend well. This will keep the lasagna from being watery.
Add the noodles and remaining 2 tablespoons oil to a large, deep pot filled with rapidly boiling salted water. Cook noodles until al dente. Drain well in a colander and then run under cold running water to stop the cooking process. Put noodles, in a single layer, on clean, damp kitchen towels. Cover with clean, damp towels.
Preheat oven to 350° F.
Ladle a thin layer of meat sauce info a lasagna pan (12 x I8 x 2 inches or 14 x I0 x 3 inches), Cover with noodles, laid lengthwise, then cover noodles with a layer of meat sauce, Spread a thin, smooth layer of ricotta over the meat sauce. Sprinkle with grated mozzarella and Pecorino Romano. Continue layers of pasta, sauce, and cheese, alternating the pasta )n opposite directions for each layer (lengthwise, then crosswise, etc.). Finish with a layer of meat sauce covered with sliced mozzarella and sprinkle with Pecorino Romano.
Bake in preheated oven for about 45 minutes or until cheese topping has melted and lasagna is bubbling.
Remove from oven and allow to rest for 15 minutes before cutting into squares and serving.