Preheat oven to 375F and chop the onion, garlic, carrots, and celery. Heat the olive oil over medium heat in a sauce pan and add in the onion and garlic. Sauté until the onions are almost translucent and add in the carrots and celery—cook until tender. Add in the tomato sauce, tomato paste, water, and seasonings. If using cooked ground beef, add it now. Heat the sauce over medium heat, then bring to a simmer over low heat and simmer for 10 minutes.
Prepare the lasagna noodles according to package instructions. If they are straight-to-oven noodles, cook the lasagna according to the instructions.
Layer the lasagna in a 9×13 inch baking dish. Start by coating the bottom with sauce. Add a layer of noodles, sauce, cheese, noodles, sauce, and cheese, repeating until you are out of noodles or you fill the baking dish.
Cook according to oven-ready noodle instructions, or 20 to 25 minutes (covered with foil) if you already prepared the noodles.