There are at least two major lessons that we can say the US learned in terms of culture and society from the Vietnam War. One had to do with the country in which the US is fighting while the other had to do with the United States and its military.
One major lesson learned was that a conflict like the one in Vietnam is fought as much in cultural and social terms as it is in military terms. This kind of war can only be won (if indeed it can be won) through winning the “hearts and minds” of the people of the country in which the US is fighting. The US has to project an image that encourages the local populace to support our cause.
A second lesson learned is that we need to ensure that morale in our own military and on our own “homefront” stays high. Both of these things were missing in Vietnam. The military was not able to maintain good morale because of things like the high number of draftees in the war. Morale fell at home as well, and the lack of support from the public helped cause the war to be lost.
These are cultural or social lessons that the US (we can hope) learned from the Vietnam War.