Admins do not have eyes everywhere, they also can't spend their entire time looking out for laggers on both teams.
I only kick/ban people for lagging if I personally fight them and they are impossible to hit down, when I know for certain that I've got a normally valid shot on them at least 3 or 4 times. I could not make these judgements on my own team, as I would have to be fighting them for a good 30 seconds. I didn't fight my own team at all, let alone for 30 seconds. The real problem in the lag kicks was not that red admins were abusing, it was that there was a serious deficit of blue admins to clean up our laggers. That is not our fault.
As for any other type of lag kick, it should only be if people's ping exceeds 400. The auto-ping kicker is only called when a player spawns, so it is possible for players to have a ping low spike and avoid the auto, in which case it's the admins job to manually remove them.
As for Kevin, did he really kick all of LBR? I want some evidence on that accusation before I move any further with this report.