Melt the butter in a heavy-bottomed Dutch oven or large saucepan over medium-low heat. Add the onions; sprinkle with salt, cover and cook 10 minutes to get them going. Uncover, add the thyme and bay leaf, and continue cooking until the onions are deeply caramelized, 1 to 11/2 hours.
Turn the heat up to medium and sprinkle the onions with the flour. Stir and allow the flour to cook, 1 to 2 minutes. Deglaze the pan with the wine and allow to reduce. Add the beef stock, chicken stock and lemon juice, and simmer, about 10 minutes. Taste the soup, and add salt and pepper as needed.
Meanwhile, preheat the broiler to high. Ladle the soup into 4 ovenproof crocks.
Mix the Swiss and Parmesan in a small bowl. Top each crock with a baguette slice and evenly distribute the cheese on top of each. Place the crocks under the broiler just until the cheese is bubbly and browning, about 1 minute. Serve hot.
From Food Network Kitchens: after further testing and to ensure the best results this recipe has been altered from what was in the actual episode.
Recipe courtesy of Melissa d'Arabian, 2010