Holy shit, I had forgotten about SOLDAT. My friends and I used to play that on the library computers in middle school.
IIRC it had a portable version that you could boot from a flash drive. Or at least the installation happened on your local user account, so it didn’t require admin rights from the school IT team.
Also, the old Dungeon Siege games. IIRC, 1 and 2 both had LAN multiplayer, where each person took control of a different character. It was basically the groundwork for the gameplay that Dragon Age Origins built upon.
Worth mentioning that some of these earlier titles were built for IPX networking, which is no longer supported by modern operated systems. I get the impression OP is asking for games with LAN gaming supporting to get recommendations, so I feel it's important to make sure they or others checking lists like this one understand they may need to go through some hoops to get some of these titles to work with a modern machine.
Yea I'm not sure of OP's ability and the requirements for games was vague. But IPX isn't that big of a hurdle, DOSBox has an emulator for it: https://www.dosbox.com/wiki/connectivity
Bigger issues would be sourcing and playing some of these games on modern systems at all. And some dedicated servers can be a pain.