In a large pot, combine lentils and 4 cups water. Cover and bring to a boil. Reduce heat to low and simmer until water is absorbed and lentils are tender, about 30 minutes. Remove from heat, then uncover and set aside.
In a separate large pot on medium-high, heat 1 tsp oil. Season turkey with salt and pepper and add to pot. Cook, turning once, until golden brown, about 8 minutes. Remove from pot and set aside.
To pot, add remaining 1 tsp oil. Add onion and saute, stirring often, until soft, about 3 minutes. Add carrots, potatoes and celery and saute for 3 more minutes. Add curry powder and cumin and saute for 3 more minutes. Stir in milk and half of lentils. (TIP: For a creamier soup, remove 1 cup of soup at this stage and puree in a blender until smooth, return to pot.)
Add turkey and 2 cups water to pot and reduce heat to medium. With 2 forks, shred turkey into bite-sized pieces. Stir in remaining half of lentils and cook, stirring occasionally, for 10 minutes; if needed, add additional water to reach desired consistency. Serve with a dollop of Greek yogurt (if using).