I see you changed it from 10,000 to 1,000 lines. That is far more reasonable, and so performance concerns are much less.
As for how I would do it, I would just add them to Sprites. E.g. if they were lines on a graph, each made of a few dozen line segments, having a Sprite for each would make it easy to manipulate them together as a line, such as hiding/showing, moving, changing their colour or other properties. And it would let Starling batch and cache them internally, for best performance.