Heat the olive oil in a large pot over medium heat. Add the pork, beef and pancetta, and cook, breaking up any clumps with a wooden spoon, until no longer pink. Add the butter, carrots, onion, celery and garlic and sauté until the veggies are soft. Add the remaining sauce ingredients and stir to combine well. Bring to a simmer, reduce the heat to low, cover and cook for 1 hour, until very tender, stirring occasionally. Uncover and cook for 30 more minutes, until reduced. Season to taste.
Preheat the oven to 425°F. Grease a 9x13-inch baking dish with cooking spray.
Bring a large pot of salted water to a boil. Add the lasagna noodles and cook according to package instructions. Drain the pasta, return to the pot, and drizzle with olive oil.
For the pesto sauce, combine the lemon juice, garlic, pine nuts, parmesan, and basil in a blender, food processor, or immersion blender. Process until mostly smooth. With the motor running, slowly add the oil until you reach a smooth and creamy consistency. It is important that you add the oil slowly and not all at once. Fold in the bechamel sauce.
To assemble the lasagna, spread a layer of bolognese sauce on the bottom of the dish, top with a layer of pasta, more bolognese, pesto, mozzarella and parmesan, and continue building, finishing with a layer of cheese. Cover with aluminum foil and bake for 20 minutes, remove the foil and bake for 10 more minutes, until golden on top.
To make the vinaigrette, combine all the ingredients except the oil in a blender, food processor, or immersion blender. As the mixture is blending, slowly add the oil to emulsify. It is very important not to add the oil all at once or too quickly.
Toss the greens, chickpeas and tomatoes with the balsamic dressing to coat. Serve the lasagna alongside the salad.