In a deep skillet or pot, cook 1 tbsp. EVOO and the pancetta over medium heat, stirring, until the pancetta is lightly browned, about 5 minutes. Add the onion, carrot, celery, garlic, bay leaf and thyme and cook, stirring, until the veggies are softened, about 5 minutes; push to the side of the pan. Increase the heat to medium-high. Add 1 tbsp. EVOO to the center of the pan and crumble in the ground beef; cook without stirring for 3 minutes. Break up the meat and continue to cook, stirring occasionally, until well browned, about 3 minutes.
Add the tomatoes and 2 cups water to the skillet; simmer, stirring occasionally, until thickened, about 30 minutes. Discard the bay leaf; season with salt and pepper. Remove from the heat; let cool.
Meanwhile, in a medium saucepan, melt the butter over medium heat. Add the flour and cook, whisking constantly, for 1 minute. Whisk in the milk in a steady stream and simmer for 2 minutes, whisking. Remove from the heat, stir in 1 cup Parmesan and season with salt and pepper. Let cool, stirring occasionally to prevent a skin from forming.
In a pot of boiling, salted water, add the remaining 1 tbsp. EVOO and the lasagna noodles. Cook, stirring, until al dente. Drain and transfer to a bowl of cold water.
Preheat the oven to 400 degrees . Grease a 9-by-13-inch baking dish; add 3/4 of the cup meat sauce to coat. Add a layer of noodles, overlapping slightly. Top with 1 cup of the meat sauce, then a layer of noodles; add 1 cup of the bechamel, spreading to coat. Repeat the layers. Add a fifth layer of noodles and top with the remaining meat sauce; dollop with the remaining bechamel. Cover with greased parchment, then wrap the pan with foil. Bake for 1 hour; uncover and sprinkle with the remaining 1/4 cup parmesan. Bake for 15 minutes more. Loosen the foil; let stand for 30 minutes before slicing.