Preheat the oven to 450 degrees F. Lightly coat two baking sheets with cooking spray.
Arrange the zucchini and eggplant slices on a large piece of paper towel. Sprinkle on both sides with ½ teaspoon of salt. Gently press another piece of paper towel on top of the vegetables and let sit for 20 minutes to draw out the extra liquid.
Rinse the salt off of the zucchini and eggplant slices and pat dry. Combine in a bowl with the portobello mushroom slices and toss with 3 tablepoons of olive oil.
Arrange the vegetables on the prepared baking sheets. Cook until the vegetables are tender and starting to brown on the underside, switching position of the baking sheets halfway through, about 20 minutes. Let cool, then roughly chop the vegetables.
While the vegetables are cooking, bring a large pot of salted water to a boil. Add the lasagna noodles and cook until just tender. Drain the noodles, gently rinse with cold water and lay on a kitchen towel, separated from each other.
Heat ½ teaspoon olive oil in a medium skillet set over medium heat. Cook the onion until tender, 4 to 5 minutes. Add the garlic and cook for 30 seconds.
In a medium bowl, stir together the onion mixture, ricotta cheese, parsley, pepper and ⅛ teaspoon salt.
Arrange a few lasagna noodles on a cutting board. Spread a heaping tablespoon of the ricotta mixture along the length of each noodle. Top with a generous ¼ cup of the chopped roasted vegetables.
Starting at one short end, tightly roll up the lasagna noodle and filling.
Turn the oven to 400 degrees F.
Prepare a 9- by 13-inch baking dish by spreading 1 cup of marinara sauce on the bottom. Arrange the lasagna rolls, seam side down. Repeat with the remaining lasagna noodles and filling.
Spread the remaining 1 ½ cups tomato sauce on top, and sprinkle with the Parmesan cheese.
Cover with foil and bake for 25 minutes. Remove the foil and bake for an additional 5 to 10 minutes, or until the cheese is melted. Remove from the oven and let cool for 5 minutes before serving.