In a large Dutch oven or other heavy pot, heat oil over medium. Add carrots, onion, and garlic and cook, stirring occasionally, until beginning to soften, about 6 minutes. Add mushrooms and season with salt and pepper. Cook until mushrooms are softened and golden brown at edges, about 8 minutes.
Add thyme, lentils, and 7 cups water; bring to a boil. Reduce heat, partially cover, and simmer until lentils are tender, about 25 minutes. Stir in soy sauce and season to taste with salt and pepper. Serve soup topped with yogurt.