Preheat the oven to 350°F (177°C). Grease a 9×13-inch baking dish with a small amount of oil (3-quart dish).

Heat the olive oil in a large skillet over medium heat. Add onions and mushrooms and cook, stirring occasionally, until the onions become translucent, about 10 minutes. Add the garlic, spinach leaves, and ¼ teaspoon of salt. Cook, stirring as needed, until the spinach is bright green and wilted.

In a medium bowl, combine the ricotta cheese, eggs, ½ teaspoon of salt, and ¼ teaspoon of pepper until well blended.

Spread 1 cup of pasta sauce over the bottom of the baking dish. Arrange three noodles lengthwise to cover the bottom. Spread half of the ricotta mixture over the noodles. Sprinkle with one-third of the parmesan and one-third of the mozzarella. Add half of the spinach mixture, then top with about ½ cup of marinara sauce. Add a second layer of noodles and repeat with the remaining ricotta, another one-third of the parmesan and mozzarella, the remaining spinach, and another ½ cup of sauce. Finish with a third layer of noodles and top with the remaining sauce, parmesan, and mozzarella.

Loosely cover the lasagna with aluminum foil and bake for 30 minutes. Uncover and bake an additional 10 to 15 minutes until the cheese is bubbly and browned around the edges. For a cheesy, golden-brown top, slide the lasagna uncovered under the broiler for 1 to 2 minutes. Let it sit for 5 to 10 minutes to set before serving.