Targon:
Mount Targon
Worships Targon
Targon is the head of the pantheon of celestials
https://boards.na.leagueoflegends.com/en/c/gameplay-balance/cfEdVAJd-welcome-to-the-aurelion-sol-qa?comment=008c0000
Targon refers to the empire -- the Aspects collectively. (Not an individual person).
Also, where did you get the information that Zoe and Taric worship Targon? In truth Zoe was a Lunari and Taric a Demacian.
Solari:
Mount Targon
Worships the celestial of the sun>
Lunari:
Mount Targon
Worships the celestial of the moon
I wouldn't say that they worship the celestial, more like the Moon and the Sun itself.
Lightbringers:
Demacia
Worships the Light
Some high rank members are called Radiant Ones, Illuminators, Sentinels, and they spread the light
The name of the religious order is Illuminators, not Lightbringers and Radiant Ones is the name of the warriors:
While in the capital, she continued her altruistic efforts, working to help those in need alongside a charitable religious order of Demacia known as the Illuminators...During her stay, she befriended a knight of the Radiant Ones, the warrior order of the Illuminators, named Kahina.
and about "Sentinels" even though Lucian's order could be connected to them, it isnt confirmed. Kayle is in limbo right now. The Veiled Lady seems to be connected to their religion, but again, it isnt confirmed.
The Great Balance:
Ionia
Maybe worships Karma
Believes all things should be in balance
Karma is refered as a "religious leader", I would say that they worship the Spirit of Ionia and revere others spirits, as the Spirit of the Dragon, instead.
Cult of The Void:
Woships the Void
You forgort to mention that they're in Shurima.
Anivia:
Freljord
Worships Anivia
Believes in hope, life, and change
The Notai and the Avarosans have different visions about Anivia:
They say she is a phoenix, with icicles instead of feathers—her wings borne on frigid wind, brrrrrr! But we Notai know, it is hope that carries Anivia, and that she is not a guardian of our realm, as the Avarosans say. She is freedom. She is the spirit that fills you as you follow your passion, no matter how mean the world is.
.
Volibear:
Freljord
Worships Volibear
Believes glory can only be found through combat
It isnt confirmed that the Winter Claw worship Volibear, they're considered separeted forces in Ornn's color story.
Frostguard:
Freljord
Worships the Watchers
Believes the Watchers, who are secretly Voidborn, will conquer the world, and that they will be given the Watcher's powers and become Iceborn
That was completly retconed, first, most of the Frostguard already are Iceborns, second, they worship the There Sisters, not the Watchers, in truth, they consider the Watchers an ancient evil that was defeated by the Iceborns, and even check if the Watchers's "seal" isnt getting weakened. All that I said can be found in The Eye of the Abbys and Lissandra's lore.
The Sun:
Shurima
Worships the Sun Disk
The Sun Disk It is connected to the power of the celestials and can give that power to mortals
Again, I believe it is the Sun itself, not the Sun Disc.
Wolf:
Noxus
Worships conquest and Death
Not sure if the worship of the Wolf is connected to conquest.
Godwillow:
Worships nature
While the God-Willow might have been worshiped, after Ivern cut it down, I think that this "cult" ended, if it exist at all.
Aatrox:
Worships Aatrox
Believing that offering a chosen to wield Aatrox would bring their tribe mercy
Sources?
Tears of Life:
Fromerly Blessed Isles
Worships Life
Buries dead with a drop of water from the Blessed Isles
The name is Brethen of Dusk and they seem to have more to do with afterlife than life, even if heal the living was one of their duties:
Yorick agreed to journey to their monastery, and there, he learned the ways of the** Brethren of the Dusk** and the true significance of their trappings. Every monk carried a spade as a symbol of their duty to conduct proper burial rites, which ensured souls would not lose their way. And each brother wore a vial of water drawn from the Blessed Isles’ sacred spring. These Tears of Life represented the monks’ duty to heal the living.