In a large pot, heat the olive oil over medium heat. Add the diced onion, carrots, and celery, and sauté for about 5-7 minutes until the vegetables are tender.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the rinsed wild rice to the pot, followed by the turkey broth, thyme, sage, and bay leaf. Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for about 45 minutes, or until the wild rice is tender.
Once the wild rice is cooked, stir in the shredded turkey, heavy cream, and chopped spinach or kale. Allow the soup to heat through for about 5-10 minutes.
Remove the bay leaf, and stir in the lemon juice. Season with salt and pepper to taste before serving.