There are many lessons to be learned from this war. However, as a historian (rather than as a military leader or a political leader) I would say that the main lesson to be learned is that the main goal of a historian is to explain the past and that this goal is difficult to accomplish in any objective way.
Students often think that history is about facts and dates. They think that it is about describing what happened in the past. However, that is not really true. Instead, history is more about explaining the past. It is not interesting to know that the US pulled out of Vietnam in 1973. Instead, it is interesting to know why the US pulled out. In other words, it is more important to analyze than to describe.
What Vietnam shows us is that it is very difficult to do this in many cases. The main historical issue in the Vietnam War is why the US lost. But this can be answered in a number of ways and none of the answers is demonstrably correct in objective terms. For example, some might say that we lost the war in Vietnam because the American public was not sufficiently supportive of the war. Others say that the problem was poor strategy. Still others say we lost because the war was essentially unwinnable. Historians have to try to determine which of these is true so they can know what the war’s lessons are. Yet they must be aware that it is exceedingly difficult to determine which factor is most responsible for the loss of the war. This is the main lesson for a historian to learn.