In your opinion, does a lip-sync performance contain the same authenticity as a performance
that includes live singing? Why or why not?

To be entirely honest with you, it depends. If the person lip syncing is telling the story differently, for example through dance then yes, it does (they need to show the emotion and expression through bodily movements). However, if the person is just standing there lip syncing than no, the person lip syncing's actual voice would explain the story, emotion and expression of the song much better.

right of the table i believe