Heat the oil in a large saucepan or Dutch oven over medium heat. Add the leeks and cook, stirring occasionally, until they begin to soften, 3 to 4 minutes. Add the tomatoes and cook, breaking them up with a spoon, for 5 minutes.
Add 6 cups water and bring to a boil. Stir in the sweet potatoes, kale, lentils, thyme, 1 ½ teaspoons salt, and ¼ teaspoon pepper. Simmer until the lentils are tender, 25 to 30 minutes.
Spoon into bowls and top with the Parmesan, if using.