halldojo: You can use LAN for multplayer without any client or authentication, it kinda goes without saying if you are playing online that you would need to connect to some sort of a service for that and for that you "need" to authenticate and I assume the easiest way for the dev team of the game is to use the built in authentcation of clients like Galaxy, steam, origin etc.
ambient_orange: thats now how it works.. All older games which work in multiplayer DOESNT have any servers because game devs shut it down decade ago! But multiplayer NOT LAN, still works!
Example: quake3
Well this is kinda how it works, you are talking about a client-server architecture, that has nothing to do with LAN other than it could be located on a LAN, LAN means Local Area Network, it is a range of IP addresses that are on the same network defined by the subnet mask, you are describing dedicated online servers, LAN is something else.
Multiplayer can be played both online (Making it a Online multiplayer, where there is a Server-client architecture, here the server component is spun up online (D3)) and also on your local network (Making it LAN multiplayer, this can be both Client/server-Client or Server-client architecture, this is where one of the clients is also a server or there is a dedicated server that clients connect to (Terraria if memory serves, quake etc)).
LAN means you play multiplayer on your local network, when it comes to solutions like Hamachi and NeoRouter there is a virtual private network that is created to simulate a LAN for computers that or on different networks.