Heat oil in a large pot over medium heat. Add onion and salt; cook and stir until softened, about 5 minutes. Reduce heat and add cayenne; stir for 30 seconds. Stir in tomato paste for 20 seconds. Pour in water.
Increase heat to high and stir lentils, rice, bulgur, garlic, and mint into the pot. Bring to a boil; reduce heat to medium-low. Cover partially and cook, stirring occasionally, until lentils are very soft, about 35 minutes.