Alright, quick recap (massive SPOILERS for the games/books follow):
The Council and Conclave exist at the start of the books, they're an entirely legitimate organisation, a union of magic users, who are there to serve the Northern monarchs. Of course, mages are very ambitious, and some of them, led by one Vilgefortz of Roggeveen, stage a coup at Thanned island during one of the meetings, and are backed by Nilfgaard and, by extension, the Scoia'tael. Shit hits the fan, the plan doesn't really work out, the traitorous mages go into hiding, and the Council and Conclave are disbanded.
This then leads to a secret organisation, the Lodge, being formed by Philippa Eilhart and some other sorceresses. The goal of this new organisation is to work towards what they think is best for magic users. What they wish to do is create a Northern empire, whose ruler is essentially the puppet of the Lodge. By the end of the books, they've failed to do that, but the organisation is still functioning and remains undiscovered. What's strange is that in TW1, it's treated as something a lot of people are aware of, even Geralt finds out about it and Triss even talks about it openly, yet in TW2 it's as if that never happened, which might be the source of your confusion, tutux. I guess CDPR retconned that whole thing.
Regardless, in TW2 (nobody knows about the existence of the Lodge) it turns out the Lodge's new plan, after failing to accomplish their previous one in the books, is to 'dethrone' Demavend and place someone under their influence as a ruler there, effectivey creating a state under the control of the Lodge. At the same time, it is decided that the Council and Conclave need to be reestablished - a reaction to the series of assassinations that have occured. It is to be done during the meeting at Loc Muinne. It is there that the Lodge and its members are unveiled and, based on the player's action, either another witch hunt against all magic users ensues, or the Council and Conclave are reestablished, while only the Lodge members become outlaws.