In total there are 4 council member, the chairman and you. You would need 5 lethal poisons in total but you can only get 4 (3 by loadout and 1 in the level). The suggestion is to add one or more two lethal poisons to the level so we can poison the entire council.
It would also require that while they are choking the others keep drinking instead of staring at the one choking.
Edit: Im aware you can emetic poison them, but i want to LETHAL poison them all.