She has an extreme managerial, economic, and efficient personality. She's used to getting what she wants. Joanne wasn't abused, tortured, or twisted in any way when she was young. Privileged and superiority complex was hardwired into her head around the time she was five or six years old, and she's never been the same. She's always known that she was destined to lead the Vault 8 Citizens, and that power has gone to her head.
She's been the leader of Vault City for many, many years, and she's seen the worst that the wasteland has to offer - but rather than taking sympathy on the poor souls that have come to Vault City for protection, she has instead taken the view that these "outlanders" were simply not strong or smart enough to achieve what Vault City has, and thus, are inferior. She tends to work too much and too hard, and she sees all her time as precious, so she has little patience for socializing without a purpose (i.e., if it doesn't involve politicking, she's going to be working late at the office instead) or for people dropping in and wasting her time. Though Mentats are banned in Vault City, one can use the Steal skill and discover that she carries some.
In the elections that occurred after the destruction of the remnants of the United States government, Senior Council Member McClure was appointed First Citizen and Lynette retired to honorary council member status. With her new free time, she traveled south to NCR and met the NCR President. She was responsible for much of the legislation that followed in the years between NCR and Vault City .
As expected, Lynette has had no positive romantic relationships up until her potential relationship with Westin from NCR in the endgame of Fallout 2. She's had little time for anything other than her job, and that's her focus - if anyone throws her job or decisions into question, she takes it as the worst sort of personal attack.
Lynette uses any negative situation involving outlanders to reinforce her beliefs and disregards or ignores any positive aspects: she's single-minded and set in her ways. The fact that she (and Vault City) had an "environmental welcome mat" stretched out for them (with the GECK) when they emerged from Vault 8 meant they suffered little hardship in comparison to other struggling communities, but this simply doesn't factor into her thinking. She believes that Vault City and the Vault citizens have survived and thrived because they are a superior breed of human - smarter, better, and more capable than the human trash that prowls the wasteland.
She is so single minded that when informed of the Enclave's defeat she merely inquires as to the strength of their power armor and how it could help solidify Vault City's supremacy.
Solve the Gecko powerplant problem: Lynette recruits the Chosen One to "solve" the problem of radiation being leaked from the Gecko powerplant, but her idea of "solving" the problem is to shut down the plant and/or killing the ghouls.
Effects of player's actions
It is important that the player be polite to Lynette at all times. Being overly rude at any time, or questioning Vault City's policies and her decisions, can result in the player being thrown out of Vault City for good, cutting off several important quests. Even if the player attains citizenship, Lynette will still revoke it and kick them out if she gets angry. When talking to her, never question Vault City's usage of "servants", never agree with Thomas Moore or suggest his murder, do not ask about Vault City's attitude towards outsiders, and never suggest Vault City and Gecko cooperate. Doing any of these things can get the player thrown out. If Lynette's expression ever turns hostile, it's best to end the conversation right away before you say something you'll "regret".
Lynette is at first highly suspicious of the Chosen One's knowledge of the G.E.C.K. and Vaults, and demands an explanation. Once she finds out the Chosen One is telling the truth, her attitude quickly changes. This can be shown through showing the Vault 13 jumpsuit to her, and then letting her inspect Vic's water flask. She takes a somewhat more honorable role in rooting out John Bishop's connections to NCR and the Raiders.