When you run a livestream in Vito, a copy of the stream is saved to your video library automatically with the visibility set to Collaborators only. If you like, you can change this to be visible to Participants so they can watch the recording on demand.
You can also request to download a copy of the original video file. Currently this can be done from the admin pane. Click on the Content tab and choose Videos from the drop-down. Navigate to the recording of the livestream and click on Request download near the bottom of the screen. It may take a few minutes to retrieve the file depending on its size.