Lin Dai-yu is the doomed, poetic, beautiful heroine of the Red Chamber Dream, the paternal cousin and beloved of the protagonist, Jia Bao-yu. Bao-yu and her share a common love based on their dislike of the world and its treacherous ways. They both wish to leave the world behind, and in the end they both do.
That of course, does not come until the spiralling tragic end of the book. Early on, when we meet Dai-yu, she is a young orphan, going to live with her cousins. She is not yet a teenager, but already gifted with a rare and beautiful literacy. Although still sad, she manages to have a good time, as her, Bao-yu and his other cousin, Xue Bao-Chai, together with their friends, spend their time chatting, joking and writing poetry together. Although Lin and Xue have opposite personalities and are rivals for Bao-yu's affections, they are genuine and close friends. Even at this early stage, however, Lin still seems to have a profound sense of her own mortality, and of the transience of the world around her. In one famous scene, she buries some flowers while reciting a poem that she composed.
As the story progresses, Dai-yu and Bao-yu never manage to reconcile or express their love for each other, and they often end up fighting or arguing with each other when they try. This causes Lin to be driven further into a cycle of mental depression and physical illness.
By the end of the book, Bao-yu's relatives decide that the boy needs a wife, and decide against the sick Dai-yu, instead choosing the more extroverted and happy Bao-chai. They trick the temporary witless Bao-yu into marrying Bao-chai while thinking he is marrying his true love, Dai-yu.
Aware of the marriage, but unaware that Bao-yu is being tricked, Lin dies of heartbreak, in the form of tuberculosis. When Bao-yu hears of this, he decides to leave mundane life behind and go back to the essence.
This plot, of doomed love on earth, is explained in a framing story, as being part of a debt of tears, that Bao-yu and Dai-yu were together in a past life, and that she owed him a lifetime of tears for his kindness in a previous life.
Although the amount of literary criticism (in English) on the Red Chamber Dream is not the same as it would be on a modern English language novel, there is still quite a bit, and there is quite a bit of writing on the psychological and cosmological significance of Lin in the story. I have seen plenty of internet discussions on such issues as Asuka Langley Soryuu vs. Rei Ayanami, and reading Doctors of Literature discuss the issue of whether Xue or Lin was the true heroine of the novel is very similiar, although thankfully usually more restrained and usually with no mention of their physical attributes. I was recently reading a book discussing Lin, who classified her as a whiny, neurotic, sarcastic selfcentered poser; while my own professor mentioned her sensitive nature, beautiful poetry and ready wit. I myself tend more to the latter opinion. But in either case, the different ways of looking at the characters are manifold, even if you can seperate the real from the false.