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Step 1: Cook the lasagna noodles according to package instructions.
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Step 2: In a large pot, cook the ground beef over medium heat until browned, breaking it up into small pieces as it cooks.
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Step 3: Add the onion, garlic, carrot, and celery to the pot and cook until the vegetables are softened.
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Step 4: Add the crushed tomatoes, salt, black pepper, basil, and oregano to the pot and stir to combine.
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Step 5: In a separate saucepan, make the béchamel sauce by melting butter over medium heat and whisking in flour to make a roux.
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Step 6: Slowly add milk to the saucepan, whisking constantly, and bring the mixture to a simmer.
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Step 7: Remove the béchamel sauce from the heat and stir in Parmesan cheese.
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Step 8: To assemble the lasagna, spread a layer of the meat sauce in the bottom of a baking dish, followed by a layer of lasagna noodles, then a layer of béchamel sauce, and finally a layer of grated Parmesan cheese.
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Step 9: Repeat the layers two more times, ending with a layer of béchamel sauce on top.
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Step 10: Cover the baking dish with aluminum foil and bake in a preheated oven at 375°F (190°C) for 30 minutes.
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Step 11: Remove the foil and continue baking for an additional 10-15 minutes, or until the top is golden brown and the lasagna is hot and bubbly.