Position a rack in the top third of the oven and preheat to 425 degrees F.

Add 2 tablespoons of the oil to a large Dutch oven and set over medium heat. Add the sausage and cook, stirring and breaking up the meat with a wooden spoon, until lightly browned and no longer pink, about 6 minutes. Remove the sausage from the pan with a slotted spoon and place in a bowl. Set aside.

Add the butter to the Dutch oven and melt over medium heat. Add the flour and cook, stirring frequently, until lightly browned, about 2 minutes. Whisk in the milk, a large pinch of salt and a few grinds of pepper. Cook, stirring frequently, until the sauce thickens and is the consistency of a thin gravy, 6 to 8 minutes. Stir in the pesto and ¼ cup of the Parmesan and set aside to cool slightly.

Meanwhile, bring a large pot of salted water to a boil. Cook the lasagna noodles 1 minute shorter than the package directions for al dente, about 7 minutes. Use a slotted spoon or spider to transfer the noodles to the sauce in the pot. Toss to fully coat and make sure the noodles don’t stick together. Reserve the pasta water.

Add the cooked sausage, spinach, 1 cup mozzarella and 1 cup pasta water to the pasta and stir to combine. If the sauce seems too thick add another ¼ cup pasta water and toss until everything is smoothly coated.

Beat the egg in a large bowl and then stir in the ricotta, remaining ¾ cup Parmesan, lemon zest, half the basil, a large pinch of salt and a few grinds of pepper.

Brush an 18-by-13-inch baking sheet with the remaining 1 tablespoon oil. Pour the pasta mixture onto the baking sheet and spread evenly. Dollop the ricotta mixture over the pasta, then sprinkle with remaining 1 cup of mozzarella. Bake until the cheese is melted and begins to bubble on top, about 20 minutes.

Turn the broiler to high. Broil the lasagna until the cheese begins to brown, about 3 minutes. Sprinkle with the remaining basil and let stand for 5 minutes before serving.