In my opinion a foundation story, like The Rape of Lucretia, is meant to communicate a warning and is meant to tell a story.  Foundation stories are what gives a civilization its identity.  Livy used this story to show the romans that if they continue down their current path and establish an emperor then they will be right back where they started.   The Rape of Lucretia was first written to start a revolt against the king and to create the roman republic way back to around 509 B.C..  Livy pasted the story back around to the roman people right around 27 B.C., almost 500 years later, when they were trying to create the Roman Empire.  A foundation story can tell the story of the past while also predicting the future.  Even though no one knows if the story of Lucretia is real, it still tells how kings, or people in charge, can be cruel and manipulative and can hold their power over you.  And even if we don’t know if her story is true, she still symbolizes something.  She symbolizes Rome and her ability to fight back.  A foundation story like Lucretia’s can also be used to predict the future.  Because we are only human and don’t learn from the past, history is doomed to repeat itself.  That is why Livy brought her story back up when he did because he knew this and was trying to prevent it.