Rinse the wild rice under cold water, then simmer it with 3 cups water and ½ teaspoon salt in a covered saucepan for 45 to 50 minutes, until chewy and split open. Drain and fluff with a fork.
Dice the onion, carrots, and celery into ¼- to ½-inch pieces, slice the mushrooms, mince the garlic, and shred the chicken into 2 cups.
Melt the butter in a Dutch oven over medium heat. Sauté the onion, carrots, and celery with a pinch of salt for 6 to 8 minutes, add the mushrooms and cook 5 to 6 minutes more, then stir in the garlic for 30 seconds.
Sprinkle the flour over the vegetables and stir constantly for 1 to 2 minutes, until no dry flour remains and the roux stays pale.
Whisk in 1 cup of broth to form a smooth paste, then whisk in the remaining broth in stages. Add the bay leaf, thyme, sage, salt, and pepper, and simmer partially covered for 20 minutes.
Discard the bay leaf, then stir in the chicken and cooked rice and simmer 5 minutes. Reduce heat to low, stir in the half-and-half and warm without boiling, then add the lemon juice and season to taste.
Ladle into warm bowls, sprinkle with fresh parsley, and serve right away.