Rinse lentils, strain and place in a large pot with 5 cups of water. Bring mixture to a boil, simmer and cook covered until the lentils are tender but not fully cooked, about 15 minutes. Most of the liquid should be absorbed.
Rinse the rice, then transfer to the pot of lentils and season with salt. Add 2 cups water, bring to a boil, then reduce to a simmer and cook covered until the rice is tender, about 18 minutes. Remove the pot from the heat. Allow the rice to rest in the pot for about 5 minutes, without opening the lid, to absorb all the liquid and steam.
In a separate large pan, heat two tablespoons of olive oil on medium heat and fry the chopped onions until golden brown, about 10-15 minutes. Transfer on top of the lentils and rice mixture, add cumin and toss to combine.
In the same large pan used to cook the onions, heat the remaining olive oil on medium heat and fry the sliced onions until golden brown and caramelized, about 15 minutes. In the last couple minutes of frying the onions, you can turn up the heat to high to get a crispy texture.
Serve the caramelized onions on top of mujadara with yogurt and mint, if desired,