I have not seen this reported before.
Are you shutting down all non-essential programs (especially anti-virus) before starting the game? Firewalls can also cause conflicts (generally on startup or loading screens, though), and network monitoring/mapping software can also cause connection issues.
Try exiting out of the Steam client, and starting the game directly from the '..\SteamApps\common\Divinity Original Sin 2\bin\EoCApp.exe' program file, by right clicking and running as administrator.
Try verifying local files: in the Steam library, right click on the game and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Cache...' button.
For joining an existing game, did the host go into the Gameplay section of the options, and enable LAN visibility? If so, you should be able to select Campaign, Join Online Game, then if required switch to LAN at the top, rather than Online.
