Preheat the oven to 425 degrees F.
Separate the Swiss chard stems from the leaves and finely chop the stems; you'll have about 1 1/2 cups of chopped stems. Heat the oil in a large, heavy saucepan over medium-high heat until hot. Then stir in the stems, garlic, onions, 1 tablespoon salt and 1 teaspoon pepper. Cook, stirring occasionally, until the vegetables are golden, about 10 minutes. Stir in the flour until combined. Whisk in the milk and bring to a boil. Boil, whisking occasionally, until thickened, about 8 minutes. Remove the sauce from the heat and let cool slightly.
Carefully puree the chard leaves in the blender with 1 1/2 cups of the sauce until smooth. Pour into the saucepan and add half of the cheeses.
Spread about 1 cup of the sauce on the bottom of a 13- by 9-inch baking dish. Layer 3 noodles, leaving about 1/2 inch of space between them. Spread another layer of sauce, 3 more noodles and another layer of sauce. Scatter half of the remaining cheeses. Continue layering the sauce and the noodles, beginning and ending with the sauce, and then sprinkle with the remaining cheeses.
Cover with foil and bake until the noodles are tender when tested with a paring knife, about 30 minutes. Remove the foil and continue to bake until the cheeses are golden in spots, about 10 minutes more. Let the lasagne stand 15 minutes before serving.