In a 5- to 6-quart pan over medium heat, stir onion and garlic in oil often until onion is limp, about 5 minutes.
Meanwhile, sort lentils and discard debris, then rinse and drain lentils.
Add lentils, sweet potatoes, curry powder, cumin, 1 teaspoon salt, 1/4 teaspoon pepper, and broth to onion mixture. Bring to a boil over high heat; reduce heat, cover, and simmer until lentils are tender to bite and sweet potatoes are tender when pierced, 25 to 30 minutes.