Been away from LoP, so correct me if I'm wrong.
1. Free : The games available for free to play, but it require internet connection as loading database come from their server.
2. Offline : The games available for free to play and doesn't need internet connection, but you have to download the game first.
3. Gold : Premium games of LoP. Usually have bigger data than their usual games and have long hours of gameplay. Since it ambitious development, they put the game behind paywall & available for member only, who pay certain periods of subscription. As far as I know, you can only play this via online to block someone pirated it. But it's futile anyways since some people can grab the source & share it to public.