Rainman,
Unfortunately, I don't know the answer to this. On our demo site, I know the livestream actually clears itself after a period of time. The Livestream is meant to be a temporary means of conveying a Live event and communicating with your users.. it's not like Comments or other things that are meant to be more permanent. The comments, I know, have the ability when you're logged in as admin to delete individual comments, but I haven't seen anything like this for the Livestream.
If you find a solution, let us know.. and we'll post back here if we find a better answer.
Hope this helps, even though it didn't answer your question directly.