I mean.. Author domain is domain from where you purchased the module.What do you mean by add author's domain in host?
This is not understable.
The domain here author sells his items ( that has WHMCS login page)
If you purchase something from rssstudio i.e: Lagom2 theme .
Author domain is: rsstudio.net
So
edit your" /etc/ hosts
127.0.0.1 rsstudio.net
127.0.0.1 lagom.rsstudio.net
Now when theme sends any info to author that will not pass through.