In a 3-quart pan over high heat, bring lentils and 2 1/2 cups water to a boil. Cover and simmer until tender to bite, 20 to 25 minutes. Drain.
Meanwhile, add oil, onions, and garlic to a 12-inch frying pan over medium heat; stir often until onions are golden, 15 to 18 minutes. Add rice, salt, cumin, and pepper; stir until rice looks opaque, about 3 minutes.
Stir in lentils and 2 more cups water. Bring to a boil over high heat; reduce heat, cover, and simmer, stirring occasionally, until rice is tender to bite and liquid is absorbed, 13 to 15 minutes. Serve with yogurt sauce.