I would say that the most important lesson to be learned about society and culture with regard to this war is the lesson that a democracy cannot maintain a war that is not popular. This may be true of many kinds of societies, but it is particularly true of a democratic society.
In a democratic society, the people are used to having their wishes heeded by the government. What is more, they also have the means by which to force the government to pay attention to them. That is, they are able to vote their leaders out of office if the leaders stray too far from the sorts of policies that the people prefer. This is particularly the case when, as with the Vietnam War, voters’ loved ones are being killed in a war that is becoming unpopular.
This is the most important social lesson from this war. When a democratic government tries to conduct an unpopular war, it makes its citizens very unhappy. They then put enough pressure on the government that it must, as Nixon did in 1971, try to start finding a way to make peace even if that is not what the leaders really want to do.