No, we should not always lie in order to be civil. Rather we should always speak the truth, even if it is uncivil to do so. The question is, what truths should I convey and how should they be expressed?
If someone politely requests some inconsequential vanity, I find that I'd likely, and have in the past acquiesced. That same demanded under threat of legal or financial repercussions would surely find itself objected to. (On actually writing that out, I'm not sure whether I'm pleased with it or not. I will have to further consider it.)
If it is based in fear, it is cowardly. Period.
I'd suggest at the point it becomes a demand or obligation as opposed to a request or opportunity. Especially if there is a threat or negative consequence attached explicitly or implicitly to speaking the truth.
I find honesty a virtue, and objective good. I also find spreading good will and fostering a sense of community to also be an objective good. Thus the ideal is to use civility, where possible, to decide what to honestly express. In your example, in a discussion between friends, you could probably find a way to express your honest disagreement with the previous mayor's policies, their effects, and your gratitude at the better governance of the new mayor as a replacement that served good will and community.
