Heat the olive oil in a medium saucepan or Dutch oven over medium heat. Add the onion and celery and cook for about 5 minutes, stirring occasionally, until softened.
Add the garlic and thyme and cook for about 30 seconds, just until fragrant.
Add the wild rice, 3½ cups of the broth, and bay leaf. Bring to a boil, then reduce the heat to maintain a gentle simmer. Partially cover and cook for 15 minutes.
Stir in the Lentils du Puy. Continue simmering for 15 minutes.
Add the carrots, diced tomatoes, pepper, and salt. Continue cooking at a gentle simmer for about 22 minutes, or until the lentils and wild rice are tender but still retain their shape and the carrots are tender.
Stir in the remaining ½ cup broth and the spinach. Cook for 1–2 minutes, just until the spinach wilts.
Remove and discard the bay leaf. Remove the soup from the heat and stir in 1 teaspoon lemon juice. Taste and add additional lemon juice, salt, or pepper as desired.
Ladle into bowls and serve with lemon wedges and crusty bread, if desired.