In what ways do the themes of love, lust, and desire manifest throughout the novel? How does it shape the character arcs of the novel's main characters?

Dream of the Red Chamber is widely regarded as the greatest novel of classical China. Authored by one Cao Xueqin, the book is claimed by some scholars to be based on the author's own family. The novel was written in the middle of the eighteenth century, during the last dynasty of China, the Qing Dynasty (1644–1912).
The characters primarily include members of several generations of the wealthy and powerful Chia family who occupy the two houses of Ningkuofu and Yungkuofu. The matriarch of these households is Madade Shih. Pao-yu is a twelve-year-old boy who enjoys imperial favor due to having been miraculously born with a piece of jade in his mouth. He becomes rather effeminate, as he is raised by his doting mother and female relatives. He develops a romantic interest in Black Jade, his first cousin.
When Black Jade's father is ill, she is sent to see him under the care of Chia Lien, a cousin of Pao-yu. After the death of a relative, Chia Lien's wife, Phoenix, takes control of the Ningkuofu household. Phoenix's lust for power leads her to extort money by lending at exorbitant rates. This lust for power ultimately alienates her husband, who seeks to take another wife in secret. Chia Lien's search for love in a new wife ultimately leads to this woman's suicide.
Love and desire also effect Pao-yu and his cousins. Precious Virtue, another of Pao-yu's cousins who inhabits the palace, is married to the increasingly disillusioned Pao-yu. Pao-yu's sincere love interest, Black Jade, is pretended by Pao-yu's family to be his wife in order to placate Pao-yu. Precious Virtue epitomizes the ideal woman, while Black Jade and Pao-yu have a shared affinity for drawing and poetry. She dies in devastation after her beloved cousin is married to another. Here, the desire of the family for Pao-yu's advantageous marriage ultimately leads to the demise of Black Jade (his true love).
Ultimately, those who were most engaged in lust, love, and desire bring the most shame upon the family and die in dishonor. Specifically, Phoenix's home is looted by bailiffs. The artistic and intellectual Pao-yu, who followed neither lust, desire, nor love, redeems the family by passing his imperial examinations with flying colors. However, he is nowhere to be found when called for imperial service. Allegedly he left the palace to become a bodhisattva.