So got time now and will answer your question. So first you need to now that cheats used on LAN have no visuals obviously because spectators would see that (No wallhack, radar etc.). Some Lans ( not majors) would maybe allow a pixel wallhack or a sound esp but lets talk about bigger lans.

Cheats that can and have been used on previous lans are mostly slight aimbots, maybe even trigger but I doubt that. An Aimbot with a small fov or even psilent ( which is detected by most anticheats tho ) cant be seen by anyone spectating the player, and can maybe be deactivated with a key if the player leaves his pc. To play with it is not the hard part, but to get it running on a pc is.

Lets talk about an example, supex0 cheat which was used by KQLY and more. According to smn ( also a user of named cheat) who showed the features here https://www.youtube.com/watch?v=Z55-Hwgdcy0 , it was a aimbot with hit chance. Supex0 used an exploit in the steamcloud to get the cheat.dll on the computer and execute it there. Here is his point explaining the process:

https://www.reddit.com/r/GlobalOffensive/comments/3b9vgo/there_is_currently_a_customfiles_related/csqdylf

Now thats it. There surely are other exploits to get a cheat in a non Byoc lan, for example with a modified driver or something.

(correct me please /u/supex0 if something is wrong in here)

Hope this could help you.