If you're unable to see the group or page you'd like to go live to, please ensure that you're an Admin of that page or group and double check the permissions you've granted to Lightstream in your Facebook Settings. After you've done this, please log out of Lightstream by clicking the Lightstream logo in the top left and then log back in to refresh your destinations.
Please note that due to recent changes with Facebook's requirements for streaming, you are not able to go live to any page with less that 100 followers.