the whole thing was actually a
Batman Gambit on Lolorito's part - although Teledji really did want to overthrow the Sultana and seize power for himself, having discovered a distant relative of the defunct pretender Thorne dynasty in the form of Nanamo's handmaiden Miriel which Teledji hoped to install on the throne as a puppet ruler he could control. Unfortunately for Teledji Miriel instead revealed the plot to Lolorito, who decided to manipulate things by paying lip service to him to make it look like Teledji had succeeded, but instead actually subverting Teledji without his knowledge in order to retain Ul'dah's
status quo with the Syndicate intact and the Sultana as figurehead (as Lolorito benefits more having the status quo retained), where after making it seem Teledji's assasination plot succeeded, setting up a situation where he knew Teledji wouldn't be able to resist the urge to gloat over Raubahn and thus infuriate him into snapping and thus eliminating Teledji, which is exactly what ends up happening.
The thing that Lolorito did not plan for was
us. He assumed the WoL and the Scions would behave and submit to arrest meekly and quietly, to be sent to stew in gaol for a few days until things blew over, then lo and behold, Lolorito would miraculously announce that "false alarm, the Sultana is fine, Teledji was a traitor trying to overthrow the Syndicate and the Sultanate that General Aldwyn had heroically put down, the WoL and the Scions are innocent and will be immediately exonerated and released."
Unfortunately the WoL and the Scions fleeing and taking refuge in Ishgard threw a big spanner in the works of Lolorito's plan, in that he had already announced the Sultana had been assassinated, and that the WoL and the Scions had resisted arrest and fled to parts unknown, causing confusion and chaos within Ul'dah especially when Lolorito then wouldn't confirm the condition of the Sultana as alive or dead one way or the other. Worse, Raubahn also resisted when he dueled Ilberd after killing Teledji, so Lolorito couldn't announce Teledji as being the mastermind behind the plot at that point.