Toss the carrots with the lemon juice, 1/4 teaspoon each cumin and salt, and a few grinds of black pepper in a bowl; set aside.
Heat the olive oil in a medium saucepan over medium-high heat. Add the onion and cook, stirring often, until deep golden brown, about 12 minutes. Using a slotted spoon, remove about half of the onion to a paper towel-lined plate; set aside.
Add the garlic, cinnamon, cayenne and the remaining 1 3/4 teaspoons cumin to the pan with the remaining onion. Cook, stirring, 1 minute. Stir in the rice and 3/4 teaspoon salt. Add 2 cups water and bring to a boil. Reduce the heat to low, cover and cook until the rice is tender and the water is absorbed, about 18 minutes.
Stir the lentils into the rice. Serve topped with the reserved carrot mixture and onion, the yogurt and cilantro.