In a 5- to 6-quart pan over high heat, bring 3 quarts water to a boil. Add lasagna and cook, stirring occasionally to separate noodles, until barely tender to bite, about 10 minutes. Drain pasta, immerse in cold water until cool, and drain again. Cover loosely.
Meanwhile, rinse and drain chard. Trim and discard discolored stem ends. Thinly slice stems crosswise and coarsely chop leaves. In a 4- to 6-quart pan over high heat, bring about 1 cup water to a boil. Add chard, reduce heat, and simmer, stirring occasionally, until stems are tender-crisp to bite, 4 to 6 minutes. Drain, extracting as much water as possible with the back of a spoon. In a bowl, mix chard with ricotta; add salt and pepper to taste.
In the same pan over medium-high heat, stir onion and garlic in oil until limp, about 10 minutes. Add tomatoes, basil, and oregano; cover and simmer to blend flavors, about 15 minutes. Add salt and pepper to taste.
Cover bottom of a 9- by 13-inch baking dish with a third of the noodles, then half the chard mixture, spreading it level to edges of dish. Spoon a third of the tomato sauce over chard mixture and sprinkle with a third of the parmesan. Repeat layers of noodles, chard mixture, sauce, and cheese. Cover with remaining noodles, then remaining tomato sauce and cheese.
Bake in a 350° regular or convection oven until hot in the center and bubbling at edges, 25 to 30 minutes. Let stand 10 minutes before serving.