whole idea of the Lucavi was that they were the real string pullers behind the War of the Lions (namely, they wanted to resurrect their leader, Altima (Ultima in the PSP remake) who was last trapped in the body of St Ajora thousands of years before FFT's time, ironically enough. The only way they could do that was to gather all the Zodiac Stones to transfer Altima's soul into the body of a suitable host - which was chosen to be Alma Beoulve. Besides Altima's resurrection, the Lucavi also gained the ability to come and go between the mortal realm and the spirit realm at will without requiring the use of their Zodiac Stones to summon them so for them it served a dual purpose.
The various waring factions used this is as a convenient means at trying to seize the throne of Ivalice as well - the 'true' reason behind the War of the Lions, so technically, it was a mutually 'beneficial' arrangement to both sides.)
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