During the story you'll get 3 moments where you will have to pick 1 out of 3 captains, the ones you pick are the ones that will be flagged for the "lobbying" mission. Just keep talking to the captains you picked until you get the scenes where they talk about the meeting, should be the last one in most cases. Keep in mind that the trigger for the scene might be one of the spots in their zone and not the captain himself.
Those numbers are pretty low. Here's a couple of files, one for each of the groups. They are right before the den mother fight, but you should be able to beat her easily if you use "defend" last every turn.
Pixeldrain