In a large pot, heat 6 tablespoons butter over medium heat. Add 1 chopped small onion and cook until soft, 6 to 8 minutes. Mix in two 10-ounce containers sliced mushrooms, 2 sliced garlic cloves and 3 thyme sprigs; season with salt and pepper. Increase the heat to medium-high and cook, stirring occasionally, until the mushrooms are golden and most of the liquid has evaporated, about 10 minutes. Add 2 tablespoons madeira wine or sherry and simmer until mostly absorbed, about 1 minute. Add 2 quarts chicken broth and 1 1/2 cups cooked white rice and bring to a boil, then simmer for 20 minutes. Discard the thyme. Using an immersion blender, puree the soup. Stir in 1 tablespoon fresh lemon juice. Makes 12 cups.