My response was that she ran away (you never actually find out). She could have been kidnapped, but the note ("why do you crumple that note on the fire") and the "circle on the dusty shelf where her money box used to be" suggest that she planned her escape. This is further supported by the idea that the mother could have neglected Lulu, causing her to run away. This is shown by the "dusty shelf" and the fact that she is dismissive of the narrator. "Why do you turn your head, mother?" gives us this idea. Finally, the "old rag-doll" that Lulu left on her bed could be symbolic of her lonely childhood. The fact that she left it behind could represent how Lulu has broken free of the metaphorical chains that restricted her and stopped her from being happy. The rag-doll could have also been a gift from the mother, which is why Lulu did not want it with her. Alternatively, the rag-doll could have been treasured by Lulu, and the way she left it behind could show how desperate and hurried the escape was.
WOW, I just went totally English-mode. My teacher would be so proud. I have GOT to use that in my essay