Heat the oil (or water/broth) in a medium sized pot over medium heat. Add the onion. Cook, stirring often, for 5 minutes, or until the onion is soft and clear. Add the mushrooms and garlic. Cook, stirring often, for another 5-7 minutes, or until the mushrooms have released their juices, are reduced in size, and are soft and tender.
Add the diced tomatoes, tomato sauce, Italian seasoning, salt, lentils, and water to the pot. Bring to a boil. Reduce the heat to low, cover, and simmer for 20 minutes, or until the lentils are tender. Be sure to stir the sauce at least 3-4 times during cooking (red lentils tend to stick to the bottom of the pot). When the lentils are soft, taste the sauce and add black pepper as needed. Stir in the kale. Re-cover the pot and allow the kale to cook in the sauce for 5 minutes.
While the sauce simmers, preheat your oven to 350F and lightly oil (or spray) a 9 x 13 inch baking dish. Bring a large pot of water to boil. Add the lasagna noodles and cook till al dente, following package instructions. Drain noodles.
Place about 1/3 of the lentil, mushroom, and kale mixture (this will be about 3 cups) on the bottom of the baking dish. Top with 1/2 cup grated cheese, spread out thinly. Place 4-5 lasagna noodles (or as many as needed) over this layer. Top the lasagna noodles with another ~3 cups of the lentil mixture and another 1/2 cup cheese. Top this layer with 4-5 more noodles. Top the noodles with the final third of the lentil mixture and 1/2 cup cheese.
Cover the lasagna with foil, transfer to the oven, and bake for 20 minutes. Uncover it and bake for another 15-20 minutes, or until the lasagna noodles are a little crispy at the edges and the cheese is melted. Cut the lasagna into 6-8 pieces (depending on what you're serving it with and how hungry you are) and serve.