The sentence is talking about the period of time that one is an adult, which is known as adulthood. "She is now in the stage of late adulthood." sound fine and very natural. You could also she "She is in the late adulthood stage." and "She is in the late adulthood life stage". "She is in the late adult life stage" sounds odd. This is because the "hood" is missing.

I don't like it. It provokes a question. Is she in her 50s or 80s? Why give only part of the information and not say clearly "she is in her 70s?

Yes. But I just wanted to see if I could say like that

Do you mean that she is old? You could say she has reached old age.