I'm still figuring out the lore of the champions and it was crossing my mind with the new champion Seth? he's named after a god like nasus and renekton but hes being classed as a vastian... are the vastians from the same lineage as the shurima gods or decedents of them? 
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No.
In lore no. By design philosophy kinda. Rito leaned too hard on the "anthropomorphic humanoid" concept to differentiate champions back when they were churning them out biweekly. As a result there are a lot of animalistic beings in LoL that are of no relation in origin. Even before Shuriman Ascended and Vastaya were a thing as a concept it was just a mish-mash of animal people with no relation to one another.
He is called Sett, not Seth though. Overall there is likely no connection besides the fact that some vastaya moved to the shuriman continent.
A rioter once gave an explanation that Renekton, Nasus and Azir look like this because the ascension ritual reforms the body according to the ideals of the person and Shurima has or at least had a lot of animal-symbolism in their language, so a golden hawk was likely a symbol for leadership, hence why Azir turned into a hawk with gold armor.
Shuriman Ascended are humans who have taken on the power of the sun disk and became demi-gods due to their traits. Such as Nasus's wisdom and Reneketons honor. Vastayan are an off shoot of early humans that are much more intune with the spirit world due to their ancestry with animal spirits.
Officially no, by a very narrow technicality yes, the ascension ritual in shurima originated from targon, while the vastaya are a natural species born of magic. Onto that technicality though, it's all magic and if the big bang happened in league then yeah, Vastaya are connected to Shuriman Ascended
That same site which is filled with lore, stories and most importantly, the answers to your question. It's like explained all in the first paragraph for the Vastaya race.
