No I do not use autopromote for that reason. I ensure you it is not the server specs because I run off a very good dedi.
I would still check the size of your
users.txt and
groups.txt files, just to make sure they're not abnormally huge.
Also, define "very good dedi[cated server]," because (iirc) Garry's Mod's multicore support is lackluster if existent.
There could also be some laggy operations running on
PlayerConnect or
PlayerInitialSpawn, etc. You might want to look into your addons and see what's hooking to those. Though that wouldn't explain lag with only a high amount of players.