Preheat the oven to 375 degrees F (190 degrees C).
Cook sausage, ground beef, and garlic in a large skillet over medium-high heat, stirring occasionally, until browned and crumbly, 5 to 7 minutes. Drain any excess grease.
Stir in diced tomatoes, tomato sauce, parsley, basil, oregano, and sugar. Bring to a boil over high heat, then reduce the heat to medium-low and simmer, stirring occasionally, until thickened, about 30 minutes.
When the sauce has simmered for about 15 minutes, bring a large pot of lightly salted water to a boil. Add lasagna noodles and cook, uncovered, stirring occasionally, until tender yet firm to the bite, about 8 minutes. Drain.
Stir sour cream, 1/2 of the mozzarella, Parmesan, olives, eggs, salt, and pepper together in a bowl.
Assemble the lasagna: Spread a thin layer of meat sauce evenly over the bottom of a 9x13-inch baking dish. Cover with 1/3 of the lasagna noodles, 1/3 of the remaining meat sauce, and 1/3 of the cheese mixture; repeat layers two more times with remaining noodles, sauce, and cheese mixture. Sprinkle remaining mozzarella evenly over top.
Bake in the preheated oven until sauce is bubbly and the cheese is golden brown, about 30 minutes.