Man muss im ansehen bei Lynette hoch im Kurs stehen, das geht z.b. in dem man sie, immer wenn die möglichkeit besteht, "First Citizen" nennt. Wenn man das Kraftwerk nicht gesprengt hat, dann spricht man sie am besten nicht drauf an, da das einen ziemlichen verlusst an ansehen nach sich zieht. Genau gehts erst wenn man eine Quest aus der NCR bekommt, hier mal ein Auszug aus dem
Nearly Ultimate Fallout 2 Guide:
Deliver Westin's holodisk to Lynette in Vault City.
When you deliver Bishop's Holodisk to Westin he'll ask if you're a Vault City citizen, and if you are he gives you this quest. (If you have the quest to kill Westin you can do it before you leave, since there's no additional reward once you deliver his disk.) For a successful delivery you get 1500 xp, a H&K G11 and 2 Frag Grenades, which Randal in Vault City will supply.
If Lynette thinks highly enough of you when you deliver the holodisk, she'll make you Captain of the Guard, a position which has several advantages as decribed in the Vault City section. To pull this off you need CH 8 and getting Lynette's "respect counter" high enough by adressing her as First Citizen at every turn. The easiest way to do this requires Speech 75% and being a citizen (which you obviously are since Westin gave you his disk), and can be done right before giving the disk to Lynette. Say you have a question for her, ask why they don't live in a vault, and then pick the last option to leave dialogue. Do this 10-15 times (or more if necessary) to raise the respect counter before giving her the disk. If you become Captain, you get 2500 xp for the delivery instead of the usual 1500 xp.