Brown beef and onion in a deep 12-inch 5-quart saute pan over medium-high heat for 8 minutes, breaking up the meat and cooking to 160°F. Drain excess fat.
Add garlic, basil and oregano for 30 seconds, then crushed tomatoes, the 2 1/2 cups water, salt and pepper. Bring to a simmer.
Add broken lasagna sheets a few pieces at a time, pushing them under the sauce and separating overlapping sheets. Cover loosely and simmer over medium-low heat for 16 to 20 minutes, lifting and stirring every 3 minutes until tender; add reserved water as needed.
Mix ricotta with Parmesan in a bowl. When the pasta is tender and the sauce still moves around it, spoon 8 small dollops over the skillet and scatter mozzarella between them.
Cover tightly and heat on low for 3 to 4 minutes until mozzarella melts and ricotta is hot. Rest off the heat for 3 minutes before spooning into bowls.