I’ve been looking for some myself but not an awful lot to pick from.
Lego titles are often local co-op. It takes two. These are what i’ve been playing with my daughter.
Borderlands 1 is cant remember if 2 & 3 are, but i think they may be.
Portal.
Overcooked, moving out, way out, unravel
games are i think.
Then games like party animals, cassette beasts, etc
I read somwhere diablo 4, Wwe 2k24, divinity sin, baldurs gate 3, sackboy are all local co-op too.
Currently on a bit of a retro trip, so emulating all those amazing Amiga games i used to love.
Simple gaming.
There’s a 2024/2024 data file for Sensible Soccer lol
It Takes Two
Rather want a game that I can play with kid.
It’s pretty family friendly.
Satisfactory. 7 days to die. Deep Rock Galactic are all good co-ops working collaboratively.
I dont think they are local co-op though?
I’m sure you killed it back in the day at clue.
When you say LAN, are you meaning no internet? In that case don’t think so. But then, how many are these days. I find using Steam and connecting using that service works great. My adult kids both have their own accounts and we connect that way and have audio as well as a solid connection.
I often boot up a C64 emulator to play Elite.
I remember the days of loading the 10 base T network drivers in Dos before running Quake / Doom 2 / Heretic and Hexen to play head to head. 2 hours to setup a game. At least the software wasn’t on tape though 
It was @Sithbare who was asking the question. I think he is looking for options to play couch co-op so not needing to have second PC/ copy of game.
Me and my friend have had great times in Valheim. It’s survival co-op. It’s even a very good game, though early access. It has a very good cult like fan following as well actually. But I have only ever played it with my friend. According to Steam I have logged 440 hours over the years. I wouldn’t do that if it’s shit…
Take a look at Abiotic Factor. That’s another along the same lines that gets rave reviews Magnus. Online co-op.
A few other games that I’m keeping my eye on.
Monomyth - oldschool dungeon crawler. EA currently and looks good.
Heroes of Might and Magic - Olden Era, looks to be very much along the older HOMM3 lines.
Path of Exile 2 - ARPG along the lines of Diablo 2 so players are saying. This is also EA. Currently EA and $30. Will go 1.0 and free to play in 6 months.
Drova - Forsaken Kin - which is a bit of an unfortunate name. I keep seeing foreskin for some reason. But its meant to be an excellent ARPG also.
Drova is great, particularly for anyone who remembers the old Gothic/Risen games, I did a playthrough on my channel a few weeks back:
Path of Exile is free to play.
I note that you do indeed play the odd game.
I also note that you do have a very nice narrator’s voice 
Nice channel.
Path of Exile 2.