要提高第一市民对你的好感最方便的方法如下
The best way to insure Lynette's respect counter for you is high enough is to find a loop in the dialogue where you can continually address her as First Citizen - after becoming a Citizen, the best way to do it is to keep asking her about Vault 13 (if you haven't found it), choosing the response of: "First Citizen, it’s very
important to me that I find the location of my ancestor’s Vault. If I may check the archives, I would be grateful." Loop it ten to fifteen times to be sure (you need at least a level 10 - I do it fifteen times to be sure), then just be sure not to anger her after that