In the 2003 anime series;
She is largely the same as her manga counterpart, highly intelligent, manipulative, devoted to her own ideals, however she begins to crave becoming a human as the series progresses. Her main purpose amongst the Homunculi is gathering information and traveling abroad, manipulating alchemists into creating Philosopher's Stones. Gaining true humanity is the focal point of her ambition, arguably much more so than the rest of the Homunculi.
SpoilerLust was created by Scar's brother, when he attempted to use alchemy to bring his lover back from the dead. After he was cast out from Ishbalan society as a heretic, Envy visited the wretched creature and fed it red stones, giving her human shape, and her new name. She was not the first Homunculus to bear the name of Lust, and is the third youngest Homunculus.
In the manga and 2009 anime series;
Lust is the only female Homunculus and the second to be created by Father. Due to her high intelligence and devotion to Father's plan, Lust appears to have a great deal of free reign and authority within the organization, seeming to have a position second only to Pride and on par with Wrath. Lust also has a great disdain for humans, thinking them frail, predictable and generally stupid. Moreover, she appears to take pleasure in using and throwing them away. Lust is the first to introduce the idea of Homunculi as superhuman, the next wave of evolution of humanity, and takes pride in her nature.