DUE TO CHANGES IN THE FACEBOOK API, LIGHTSTREAM IS CURRENTLY UNABLE TO GO LIVE TO FACEBOOK GROUPS USING NORMAL METHODS. PLEASE REFER TO THIS ARTICLE FOR CREATING SCHEDULED POSTS TO GO LIVE TO YOUR GROUP.
To go live on your Facebook Group or Facebook Event pages you'll want to click on the cog at the top right of the Lightstream editor to access the stream settings panel. From here you'll want to select the Group or Event page that you would like to go live to from the "Go live on" dropdown box.
Note: To go live on a Facebook Group you'll need Admin permissions at the moment.