In a bowl, toss the chopped white mushrooms with the lemon juice. In a large saucepan, combine the chicken stock with the chopped white and shiitake mushrooms and the garlic and bring to a boil; simmer over moderately low heat until the mushrooms are tender, about 10 minutes.
Meanwhile, in a medium nonstick skillet, heat the oil. Add the sliced white mushrooms and cook over moderately high heat, stirring, until golden brown and tender, about 4 minutes. Season with salt and pepper.
Working in batches, puree the soup in a blender until very smooth; return to the saucepan and whisk in the crème fraîche. Simmer for 2 minutes. Add the coriander and season with salt and pepper. Ladle the soup into bowls. Garnish with the sautéed mushrooms and chervil and serve.