Prepare wild rice according to the package instructions. This typically takes around 50 to 60 minutes. This can be done up to a day or two in advance and kept in the refrigerator until you are ready to make the soup
In a large dutch oven or heavy pot, melt butter over medium heat. Add the onion, celery, carrots, mushrooms, and garlic, and stir, sauteing until the onion has softened.
Sprinkle the flour over the sauteed vegetables and stir in, cooking for 1 minute. Slowly add the broth, stirring constantly. Increase the heat to medium-high until the soup comes to a low boil.
Reduce heat to medium and add the cooked wild rice, parsley, salt, pepper, thyme, rosemary, and shredded turkey. Simmer for 20 minutes.
Add milk, cream, and lemon juice, and cook another 3-5 minutes until hot, tasting and adjust seasoning by adding more salt and pepper, if needed. Serve immediately.