1. To prepare sauce, heat 1 tablespoon oil in a large saucepan over medium heat. Add chopped onion to pan, and cook for 15 minutes or until golden, stirring occasionally. Add garlic; cook for 2 minutes. Stir in 1/2 teaspoon salt, peppers, and tomatoes; cook 10 minutes or until slightly thick. Transfer tomato mixture to a food processor; process 1 minute or until smooth. Keep warm. Wipe skillet dry with paper towels.
2. To prepare koshari, heat 3 tablespoons oil in pan over medium heat. Add sliced onion; cook 15 minutes or until deep golden brown, stirring frequently. Remove onion with a slotted spoon to several layers of paper towels; set aside. Return pan to medium heat. Add vermicelli; sauté 2 minutes or until golden brown, stirring frequently. Set aside.
3. Combine 5 cups water and lentils in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer 30 minutes or until lentils are tender. Remove from heat; add vermicelli, stirring well to combine. Wrap a clean kitchen towel around lid, and cover lentil mixture; let stand for 10 minutes or until vermicelli is tender. Add rice and 1 teaspoon salt to lentil mixture; fluff with a fork. Serve immediately with sauce and onions.