Preheat oven to 375 degrees F. Spray a 13x9-inch baking dish with cooking spray; set aside.
Bring a large pot of water to a boil. Add ½ teaspoon salt and 1 tablespoon olive oil. Add lasagna noodles and cook according to package directions. Drain and set aside to cool slightly.
Meanwhile, heat remaining 1 tablespoon olive oil in a large skillet over medium heat. Add onion and cook, stirring occasionally, until it begins to soften, about 3 minutes. Add mushrooms to the pan and cook until softened, about 5 minutes. Season with ¼ tsp. kosher salt and freshly ground black pepper. Add garlic and Italian seasoning; cook, stirring, for about 1 minute. Add kale and cook, stirring, until wilted, 2-3 minutes. Stir in marinara sauce; cook at a low simmer for 10 minutes.
In a medium bowl, stir together the ricotta and ½ cup grated Parmesan.
To assemble the lasagna, spread 1 cup of the sauce mixture in the bottom of the prepared baking dish. Lay 3 lasagna noodles on top of the sauce. On top of the noodles, spread ¼ of the remaining sauce, then dollop on 1/3 of the ricotta mixture and sprinkle with ¼ of the mozzarella cheese. Repeat noodles, sauce, ricotta, mozzarella layers 2 times more. For the top layer, use noodles, sauce, and mozzarella, but no ricotta. Sprinkle remaining ¼ cup Parmesan on top.
Spray a piece of foil with cooking spray and cover lasagna tightly. Bake in the preheated oven for 30 minutes; uncover and bake 10-15 minutes more, until sauce is bubbly and cheese is golden brown. Let stand at room temperature for 10 minutes before serving.