Lysistrata is the latest of the core members, appearing only on the Second Time Warp. As such, Lysistrata had to start from scratch (not unlike Eurydike, who also passed away at the first time warp), building a solid medical
career and a solid logic base. Lysistrata being insane made good friends with Eurydike, and also took interest in the other insane characters out there, notably the superstars Stratonike and Kallisto.
Lysistrata, despite her relative lack of skills and experience, was nonetheless a crucial part of the imperialist plans of the Union of the Insane, as Lysistrata would be the face of the said group, and it was Lysistrata that ensured that there isn't much dissident opinions on what would be the virtual hegemony of Sunset Valley. Lysistrata, although not an imperialist nor had any imperialist motives, played along, as nobody was getting hurt (aside enemies of the core members, notably Christopher Steel) and the fact that some sims viewed their dominance as better than that of the Altos (especially the Landgraabs, despite the normalization of relationships with the Altos)