Melt the butter with the oil in a medium skillet over medium heat. Add the onions, sugar, and some salt and pepper. Cook until the onions become deep brown and sticky, about 20 minutes, stirring every 4 or 5 minutes (if the onions color too quickly, reduce the heat to medium-low).
While the onions caramelize, make the rice. Heat the remaining tablespoon of oil in a saucepan over medium heat. Add the garlic and cook, stirring, until fragrant, 30 seconds to 1 minute. Add the rice and stir, cooking it until the grains begin to turn opaque, about 2 minutes. Add the water, lentils, and cumin; season with salt and pepper. Increase heat to medium-high and bring to a boil. Reduce the heat to low, cover, and cook until the rice is tender and has absorbed all of the liquid, about 20 minutes. Serve topped with the caramelized onions.