To roast vegetables, preheat oven to 400°F. Coat two baking sheets with cooking spray. Place eggplant on one prepared baking sheet and place zucchini on other prepared baking sheet; coat vegetables with cooking spray. Roast 8 minutes; flip vegetables and roast for 7 to 10 minutes more (total roasting time should not exceed 20 minutes or the vegetables will get too mushy). Remove vegetables from oven; reduce oven temperature to 350°F.
Meanwhile, while vegetables roast, in a medium bowl, combine egg, ricotta cheese, basil and 1/4 cup Parmesan cheese; set aside.
To assemble lasagna, coat bottom and sides of a 14- X 8-inch baking dish with cooking spray. Spread a thin layer of sauce (about 1/4 to 1/3 cup) on bottom of pan. Layer eggplant over sauce (use all the slices, even if you have to overlap them). Cover eggplant with half of marinara sauce and then spread half of ricotta mixture on top; sprinkle with half of mozzarella cheese. Top mozzarella cheese with zucchini and cover zucchini with remaining marinara sauce; spread with remaining ricotta mixture and then sprinkle with remaining mozzarella and Parmesan cheeses.
Bake until the bottom starts to bubble, about 35 to 40 minutes. Remove lasagna from oven and allow it to rest for about 15 to 20 minutes before slicing into 12 pieces. Yields 1 piece per serving.