WARNING: The following contains spoilers for Cowboy Bebop, now streaming on Netflix.
In the original Cowboy Bebop anime, Julia is a character with a huge presence who is also afforded very little to no agency. As the love interest of protagonist Spike Spiegel and his former best friend, Vicious, Julia primarily appears in flashbacks and in the final two episodes of the anime. As such, she is given very few -- if any -- opportunities to exist as a character independent of her value to the men in her life. This is one area where the live-action Netflix adaptation makes a significant improvement to her character.
In the live-action series, Julia's role is expanded and is given a character arc of her own. She's even set up to become the primary antagonist by the Cowboy Bebop Season 1 finale, which also introduces the character of Radical Edward, possibly setting up Season 2. While these new developments may contradict the role Julia is meant to serve in the original story as Spike's Lost Lenore, it's also a direction that promotes Julia from existing as the mere object of two men's obsessions to being her own well-rounded character.
In major contrast with the original anime, Julia doesn't spend the majority of the series in hiding to protect both herself and Spike from Vicious. Instead, she chooses to marry Vicious with the reasoning that the latter will protect her from the Syndicate. This works for a while until Vicious starts earning income independent of the Syndicate with the selling of a performance-enhancement drug known as Red Eye. When the Elders find out about Vicious' side hustle, they force him to prove his loyalty by demonstrating he'd be willing to kill Julia for them. This experience shakes Julia's faith in her husband, which motivates her to start thinking of other ways to protect herself. This brings her back to her old friend and former employer, Ana.
Based on the character of Annie from the anime (who is also a friend of Julia), Ana is a nightclub owner who originally had Julia cover for her star singer when the latter got sick. After the success of her impromptu debut with Ana's customers, Julia became a regular singer at the club, eventually getting promoted to the club's star singer. Under Ana's employment, Julia got to enjoy a stable life before Vicious and Spike -- known as Fearless at the time -- entered her life. Since meeting both men, her life got tangled up in Syndicate affairs, especially since both men ended up falling in love with her. With the instability both Spike and Vicious brought into her life, it only made sense that Julia would go back to Ana -- the one person who brought stability to her life.
In her conversation with Ana where Julia unpacks her uncertainties and concerns, the former tells her something that stays with her for the remainder of the series: "There's always a choice. I haven't survived on this sweet, spinning sphere by chance; I did it by taking power. You have to take power. You control your destiny." When Julia especially finds out that Spike is still alive and that he never came back for her, having easily believed Vicious' lies, that's when Julia takes Ana's words to heart and initiates a coup of her own.
Originally, Julia attempts her coup by forming an alliance with Mao Yenrai to have Vicious killed. This ultimately backfires when the latter learns of Julia's betrayal during his own successful coup of the Syndicate and his violent execution of the Elders. Vicious, however, does not regain full control of Julia. Instead, Julia develops a backup plan on the fly: during Vicious' violent confrontation with Spike, she incapacitates Vicious and decides to cut ties with Spike. With the Elders out of her way and Vicious now at her mercy, Julia herself decides to take control of the Syndicate.
How Julia plans to reform the Syndicate will most likely be explored in Season 2 of Cowboy Bebop. While it appears as though Julia had descended down a path of villainy by the Season 1 finale, it cannot be ruled out yet that her motivations are still coming from a desire to regain control of her life. Throughout Season 1, Julia's life was being controlled by Spike, Vicious and the Syndicate -- the latter of which no one leaves with their life, as Spike learned the hard way. With all the suffering Julia experienced by being connected to all three, it's not unrealistic that she resorted to fighting fire with fire as a way to taking power and ultimately regaining control of her own life, which is what she's been wanting from the beginning.
Cowboy Bebop Season 1 is currently streaming in full on Netflix.