Preheat the oven to 425 degrees F.
Heat the garlic and 2 tablespoons of the oil together in a large skillet over medium heat until the garlic begins to brown around the edges, 4 to 5 minutes. Add the crushed tomatoes, tomato paste, basil and 1 teaspoon salt. Fill the empty tomato can with 1 1/2 cups of water , swish it around and add it to the pan. Raise the heat to medium-high and bring to a simmer, stirring occasionally, until the sauce is thickened, 20 to 24 minutes. (You should have about 4 cups.) Allow the sauce to cool.
Meanwhile, bring a large pot of salted water to a boil.
Heat the remaining 1 tablespoon oil in a medium skillet over medium-high heat. Add the sausage and cook, breaking up with a slotted spoon into smaller pieces no more than 1 inch long. Cook until browned, about 7 minutes. Transfer the cooked sausage with the spoon to a paper-towel-lined plate to drain.
Add the lasagna noodles one at a time to the boiling water and cook until al dente, about 8 minutes. Stir very gently with a wooden spoon to prevent the noodles from sticking. Drain into a colander and rinse under cold water until they are cool enough to handle; drape over the side of the colander. (This will also help to separate the sheets so they do not stick together.)
Mix the ricotta, parsley and egg with 1/2 teaspoon salt in a medium bowl until well combined. Add the turkey and sausage and stir to combine. Set aside.
Spoon a very scant layer of sauce, about 1/4 cup, into a 9-by-13-inch baking dish and spread to coat the bottom. Line the bottom with one layer of lasagna noodles, slightly overlapping and cutting to fit if necessary. Spread half of the ricotta mixture over the noodles, then a third of the tomato sauce, followed by a third of the mozzarella and a third of the Parmesan. Cover with a third of the lasagna noodles, again arranged so they are overlapping slightly. Top with the other half of the ricotta mixture, then another third of the sauce. Add another third of the mozzarella and third of the Parmesan. Finish with the remaining lasagna sheets and top the lasagna with the remaining sauce, mozzarella and Parmesan.
Cover with foil and bake until hot throughout and the cheese is melted, about 30 minutes. Uncover and continue to bake until slightly golden brown, about 10 minutes more. Let rest for 10 minutes, cut into pieces and serve.
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