We don't generally "read about stories". We either "read stories", "read stories about" or "read about + subject".
You can read stories of people's lives.
You can read stories about people's lives.
You can read about people's lives.
If the "people" concerned have been referred to already and you know which people, then you will see "... the people's lives". You might also see "the stories" for the same reason.
You will realise by now that there are no hard and fast rules for articles. Context and meaning are very important.