What does "within a generation" mean in this context?

So, for this question you need to consider the different media and the applications of language.

In your analysis you're trying to interpret it in a scientific application, and boil the word "generation" to precise numbers as if it were written media (papers, journals, etc.).

In the documentary (original source) the author is using jornalistic language, mostly sticking to the common meaning of the word and being deliberately vague to create a more emotional effect. If there was any intent of being precise, they'd have used the actual numbers - instead of a generation, they'd have said 32 years, from 1917 to 1949.

Please note that there is indeed a difference between "a generation" and "a lifetime".

A generation is used to express the average time between the birth of a population mass and the birth of this population's offspring, so that's about 20-30 years. You often see this when you see articles about the cultural differences between the so-called "baby boomers", "generation X", "Millenials" and "generation Z", which are 4 populational groups separated by roughly 20-30 years in age. Another application of the common meaning of "generation" is when you're talking about ancestry when you have migratory movements - e.g. "I'm a second-generation Japanese" when referring to having Japanese ancestry when not being born in Japan.

On the other hand, "a lifetime" is a person or a population's lifespan, and it can span multiple generations, since people now live enough to have grandchildren and great-grandchildren.