Originally striking Nick as mysterious and alluring, the upper-crust socialite Jordan is soon revealed to lead a life entirely based upon lies. A considerable amount of her identity and pride is based on her status as a professional golfer, and yet she cheated to win her first tournament. Often times, it seems that she is dishonest in situations that have no tangible benefit to her and simply lies pathologically.
Jordan's dishonesty, like the rest of her character, is representative of the "new women" of the roaring twenties. She does not care if people think of her as dishonest and takes as little consideration in regard to her moral standing as she does with her open consumption of alcohol and attitude toward casual sexuality. Jordan's dishonesty is much the same as that of the men in upper-crust society. Blunt and cynical, she makes no attempt to adhere to the rigid standards of femininity that were expected of high-class women in the past.
Jordan's lies add to the theme of the novel: that the wealthy characters, especially those born into their status, are irresponsible, careless, and entitled.
One key example of dishonesty in Jordan's character is Nick's suspicion that Jordan cheats at golf. Jordan is a professional golfer, but apparently (at least according to Nick's narration) she feels that she can get what she wants by any means necessary; if she wants to win, she can cheat. This sense of entitlement is seen in the characters Tom and Daisy as well.
In contrast, Nick sees Gatsby as more wholesome because he has to earn his position and is not entitled. It's ironic, then, that Gatsby earned his wealth through the help of Dan Cody and through illegal activities (presumably bootlegging).
Jordan's casual attitude toward life in general (including the need to tell the truth or act morally) mirrors the carelessness of the upper class more generally. Another great example of that is Daisy's reckless behavior in running over Myrtle and then letting Gatsby take the fall; Daisy and Tom carry on with their lives as if nothing happened. Dishonesty in the wealthy characters, like Jordan, create the impression that the rich are self-interested, entitled, and reckless.
Jordan's lies further the theme of corruption that is seen in many different ways throughout the novel. All of the characters lie about their lives or live lies by their actions. Jordan cheats at golf; Tom has an affair with Mrytle; Daisy leads Gatsby to think there is a future for them; Gatsby lies to himself in thinking that he can repeat the past (with Daisy). It seems that if there was a list of all of the actions in the book each and every one could tie back to the ideas of deception or corruption in some way. Nick's narration reveals his utter disgust with everyone's behavior. He is so sickened by it all that he returns to his midwest roots and hopes to reconnect to a place with a stronger moral fiber than what he has witnessed in the East. Fitzgerald has no morally redeemable characters from the East, so Jordan is just one in the long list, and it hurts Nick because he was fond of her.
In some ways similar to the inconsistency and tendency to use other people, Jordan's dishonesty only serves to heighten the impression of her worldview based entirely on what she feels is good for her or what she wants at the moment. She is meant to be seen as amoral and selfish and her lying to Nick and to others helps to strengthen that impression.
In some ways it also connects to the fact that basically everything about her is false, both her words as well as her actions and the act she puts on for the world.