Bring lentils, onion, garlic, and 4 cups water to a boil in a saucepan. Reduce heat; simmer until tender, about 20 minutes.
Meanwhile, whisk together ginger, mustard, and vinegar in a small bowl. Season with salt and pepper. Gradually whisk in oil. Toss together carrots, parsley, and half of dressing in a bowl. Season with salt and pepper.
Drain lentils; discard onion and garlic. Toss lentils with remaining dressing in another bowl. Transfer to a platter, top with carrot mixture, and serve.