I always make either a double or triple batch of this soup. In the past few years I've been adding a few additional spices -- see notes below. Turmeric is what makes the soup so yellow in the photos -- it will be paler yellow without it.
In a medium pot with a heavy bottom, heat the oil over medium-high heat.** Add the onion and carrots (if using) and cook, stirring occasionally until starting to soften, about 5 minutes. Reduce heat if necessary to prevent browning. Add lentils and rice and stir to coat with oil. Add water, salt, cumin, and pepper. Bring to a boil, then cover and reduce heat to maintain a simmer. Cook, lifting the lid occasionally to stir, until lentils and rice are completely tender and the soup is of uniform and moderately thick consistency, about an hour. Serve hot with lemon wedges to squeeze overtop.
*At the risk of messing with perfection, I also really love the following variation on the spices: 1 teaspoon ground cumin, 1 teaspoon ground coriander, 1/2 teaspoon ground turmeric, 1/2 teaspoon ground sweet paprika.
** You can omit the oil and just combine all the other ingredients in the pot from the start. I usually do this now because I don't notice a difference, and it's a little easier. Sometimes I drizzle a little fruity olive oil onto each bowl before serving.