Simmer lentils in salted water for 45 minutes until tender. The lentils will double in size. Meanwhile, saute onions and carrots in 2 tablespoons olive oil until soft. Transfer vegetables to a large mixing bowl. Add sugar, parsley, red wine vinegar and remaining olive oil.
Drain lentils well and add them to mixing bowl. Toss well while lentils are warm. You may need to add more oil and vinegar according to taste. Season to taste with salt and pepper. Serve warm, room temperature or chilled.