Bring a large pot of lightly salted water to a boil. Cook lasagna sheets in boiling water until al dente, for about 8 minutes. Drain the pasta, and rinse with cold water. Set aside.
To make the meat sauce, heat the olive oil over medium heat in a large deep skillet. Add the ground beef, onions and garlic, season with Italian seasoning, salt and pepper, and cook until beef is well browned, about 10 minutes. Add the crushed tomatoes and tomato paste. Simmer until the sauce is thickened, 10 more minutes. Set aside.
Preheat the oven to 375˚F
In a large bowl, combine all of the Greek yogurt sauce ingredients: yogurt, mozzarella, Parmeggiano Reggiano, egg, basil, salt, and pepper.
To assemble, add 1 cup of the meat sauce to a 9x13 baking dish and spread evenly. Arrange 4 cooked lasagna sheets on top. Layer 1/3 of the Greek yogurt mixture, 1/3 of the remaining meat sauce and 1/3 of the mozzarella cheese. Continue for 2 more layers, and finish with lasagna sheets topped with the meat sauce and the remaining cheese.
Cover with foil and bake in the preheated oven for 30 minutes. Remove the foil, and bake for an additional 20 minutes or until the cheese is golden and bubbly. Let rest for 15 minutes before cutting.