No LAN mode but on PC the "host" actually hosts the game (not sure how they do TURN/STUN but it does work most of the time), so if you have all four people in the same building it should run as though it's LAN. There are server side checks for the items you find in the game so it has to run partially through a central server.
battlefield bad company 2 is a similar experience to helldivers 2, IMO, and that is LAN-able.
I can’t speak for other events, but QuakeCon and Dreamhack have had internet access (and quite good access all things considered) for a decade or more now.
Yeah the LANs I go to are online. Steam and many of the games have global browsers. Also, unfortunately, I don't think even the smaller one is literally one LAN. it's a routed network.
Or does this LAN have Internet? Where I am at LAN parties are completely offline, so genuinely curious.