In a medium pot over medium heat, add the oil, onion and ½ teaspoon salt and cook until softened, about 3-5 minutes, stirring occasionally.
Add the curry powder, turmeric, black pepper, and red pepper flakes (if using), and cook for 30 seconds, stirring constantly, to bloom the spices.
Add the water, soy sauce, lentils, sweet potato, and remaining ½ teaspoon salt. Cover and bring to a boil over high heat. Give the soup a stir, then reduce to low/medium-low to maintain a gentle simmer (covered) for about 15 minutes or until sweet potatoes are very soft and lentils have broken down, stirring halfway through.
Stir in the greens and simmer, covered, for 5-10 more minutes, or until the greens have softened. Remove from heat and stir in the lime.
In a medium bowl, whisk together the yogurt, water, lime, and salt until totally smooth.
Serve the soup topped with lime yogurt and cilantro.