Stat to increase damage on elemental attacks such as Luminous Spire

[Viridiana]

To try to answer the question, if its physical damage str will modify the damage and dex wil modify its accuracy, if its magic damage, its intelligence to modify the damage and piety to modify the accuracy.

Except that on mages, INT only increases dart damage at the moment. As such, I wouldn't expect INT to raise the damage on any GLA abilities at all.