Note: This article contains information related to the old Livescale experience, which has been deprecated, and it may no longer be applicable.
To create a private event, you can toggle off the link sharing options in the "Design" step:
The first share button allows you to share the live event link before the live starts, and the second share button is to share the link during the live.
Simply toggle both share buttons on/off as you please.
Note: At the moment, there is no way of creating a strictly private access to a live event or restricting users from accessing it.