Currently, the game requires an internet connection to login regardless of if you select online or offline, but this is set to change at launch when offline mode becomes truly offline.
That said, you can technically play the game right now without an active internet connection after you’ve selected offline and entered the game world with your character. If you still experience this “lag” while in offline and without an active internet connection then you can rule out the servers as the issue. Just know that if you want to return to the character select screen you’ll need to return to having an active internet connection prior to doing so.
Also, if you’re playing offline and have the chat enabled then maybe try disabling it first to see if that makes a difference for you.