Preheat the oven to 375 degrees F.
In a 12-inch high-sided skillet, heat the olive oil over medium heat. Add the sausage and cook, breaking it into bite-size pieces with a wooden spoon, until cooked through and browned, about 7 minutes. Add the shallots and garlic and cook until translucent and slightly fragrant, another 3 minutes. Add the lemon zest and red pepper flakes and cook for additional 2 minutes to toast. Stir in the broccoli rabe and salt; cook until the rabe is wilted, 2 minutes. Remove the mixture to a medium bowl and return the pan to the stove over low heat.
Spoon a small amount of the marinara sauce in the bottom of the skillet. Mix the remaining marinara with the sausage mixture in the bowl. Layer half of the lasagna noodles on top of the marinara, breaking them up as needed to fit the pan. Cover with half of the sausage mixture. Add 3/4 cup of the Parmesan and half the mozzarella. Layer with the remaining noodles. Cover with the remaining sausage mixture and top with the rest of the Parmesan and mozzarella and the Gruyere.
Bake until bubbly and golden on top, about 40 minutes. Cool for 5 minutes before serving.