Edith Wharton's The House of Mirth presents Lily as an extremely shallow character who desperately wants to elevate her social status through a suitable marriage. For this reason, she refuses to wed Seldon, who is her closest friend and confidante. Her inability to control the wealth she does have eventually causes her financial ruin, and her family wants nothing to do with her when rumors begin. This would imply that Lily is indeed selfish and materialistic.
However, smaller plot details shade Lily's character in a different way. Twice she denies courses of action which would solve her financial difficulties because they would contradict her ethical values, first by denying the married Mr. Gus Trenor's attempts at wooing her, and then refusing to blackmail Mrs. Bertha Dorset (the woman spreading rumors about Lily) when she uncovers another affair.
Lily is a romantic at heart, and though she desires money and social status, she also wants real love in her marriage. Failing to find this, she commits suicide at the end of the novel.
Lily is not a flat character with only shallow and materialistic qualities, but rather a well-rounded tragic heroine who cannot achieve her dreams without sacrificing her sense of self, and ends up recognizing the impossibility of her goals and refusing to go on any longer.