Place water and lentils in a saucepan. Bring to a boil. Reduce heat to medium-low, cover, and simmer until lentils are tender and liquid has been absorbed, about 20 minutes.
Heat oil in a skillet or tagine over medium-high heat. Saute onions until browned and translucent, about 5 minutes. Add garlic, turmeric, coriander, cumin, salt, and pepper. Cook and stir until fragrant, about 3 minutes. Stir in the cooked lentils, potatoes, crushed tomatoes, sweet potatoes, and carrots. Pour in vegetable broth; reduce heat and simmer until vegetables are tender, about 40 minutes.