Preheat the oven to 400 degrees F; place two baking sheets in the oven to preheat.
Drizzle the zucchini and eggplant slices on both sides with olive oil to coat. Carefully add the vegetables to the hot baking sheets--they should sizzle. Sprinkle with salt and pepper.
Roast until the vegetables are tender, 12 minutes, flipping halfway through. Remove from the oven and let cool.
Reduce the oven temperature to 350 degrees F.
While the roasted vegetables are cooling, heat the 2 tablespoons olive oil in a saute pan over medium heat. Add the sausage, breaking it up with a spoon, and cook until browned and no longer pink, 7 to 10 minutes.
In a bowl, whisk together the ricotta, parsley, egg and a big pinch of salt and pepper.
In a 9-by-13-inch baking dish, add 1/2 to 3/4 cup of the marinara sauce and spread to cover the bottom of the pan. Lay down enough lasagna noodles to cover the sauce, and then sprinkle with one-third of the browned sausage. Cover the sausage with one-third of the roasted zucchini and eggplant, spread with half of the ricotta mixture and sprinkle with one-third of the mozzarella. Repeat the sequence of marinara, noodles, sausage, vegetables, ricotta and mozzarella. For the third and final layer, repeat as before, only without the ricotta. Finish by sprinkling the Parmesan over the top.
Place the lasagna in the oven and cook until bubbly and browned on top, 35 minutes. Let cool for 10 minutes before serving.