Heat oil in a large pot over medium heat and cook onions until soft and translucent, about 5 minutes. Season with turmeric, cumin, and dry mustard and stir to combine for 1 minute.
Rinse lentils under cold running water twice in a colander and drain. Add lentils and water to the pot and bring to a boil. Reduce heat and simmer, covered, until lentils are soft, 20 to 25 minutes. Add rice and puree with an immersion blender. Add more water if soup is too thick.
Stir chard and cilantro into the soup and cook until flavors are well combined, 3 to 5 minutes. Season with lime juice, salt, and pepper.