Heat the olive oil in a skillet over medium heat. Add the diced onion, garlic, celery, carrots, and ground beef. Break up the beef and stir everything together until the beef has browned, approximately 5 minutes.
Pour in the marinara sauce along with the Italian seasoning and a pinch of salt and pepper. Stir it all together and let it simmer over a low heat for 30 minutes or until it is thick and saucy.
While the meat sauce cooks, make your white sauce by melting the butter in a small saucepan. Add the flour to the melted butter and whisk until a smooth roux forms.
Cook the roux for 2 minutes while whisking. Slowly pour in the whole milk and whisk continuously until the mixture thickens into a smooth sauce.
Assemble the lasagna in an oven-safe skillet. Add half the meat sauce to the skillet, followed by a single layer of lasagna sheets. You can break the sheets to fit the size of the skillet. Then, add a layer of the white sauce over top. Repeat this for one more layer.
Top with the mozzarella and Parmesan. Bake for 25-30 minutes. Allow to stand for 5 minutes before serving.