I'm pretty sure Lolorito's end game is Omega. The question is how he can distract the other GCs so he can get free access to it. Frankly I suspect he thinks that if he can gain control of it with the scions and WoL out of the way, he will be in a position to dictate terms to the other city states. We are talking about a weapon designed by the Allag to take on Bahamut.
Now I won't be surprised if it runs deeper than that. However I'm pretty sure Omega is key. The Monetarists have moved out of the relative safety of their previous position to seize direct power. They will know they have drawn a lot of hostility and running around the open world talking to npcs shows their current influence outside Ul'dah is limited. Not so much that you can do whatever you want. Your still a wanted fugitive by Ul'dah law and that puts pressure on the other city states. But enough that they can't easily hunt you down or demand the other city states detain you.
