How exactly would they go on about absorbing said paleolithic peoples? I imagine things will be pretty awkward even should the Westerlanders come in in-peace and not raid
They may think that they’re “demons” because metal armor, especially iron, is beyond them
How would religion, especially one as organized as the Faith of the Seven survive and adapt? I imagine that some place will be the area for a new High Septon and it may not even be in the Westerlands
Also, what would happen to the main Lannister family? I imagine that Jaime will be pressured to become King or Prince of The Westerlands/Rock
Or Joffrey(what a disaster)will become King.....and Tywin has to spend time telling people not to follow his insanely violent and violently insane orders
The Paleolithic peoples do not have either the numbers or the technology to meet the Westerosi on even subordinate terms.
They will be destroyed or assimilated. Its hard to visualize-but the population densities as well as the technological disparity mean that the paleolithic peoples aren't even really going to be factor.
The Faith of the Seven would likely develop the notion the Seven brought them to this world for the sake of spreading the faith, and for House Lannister ruling said world. Though as time goes on I expect splinter sects will emerge which will form their own religions.
Yeah Jaimie will be pressured into being his father's heir. No one to marry him off to except a vassal(unlike Eowyn-which is where Hear Me Roar seemed to be going), as for Joffrey-Cersei's children will likely be given Castamere or some other seat as there is no point in having a Baratheon king anymore. Cersei and Tyrion alongside the various Lannister cousins likely marry various vassals or otherwise live uneventful lives(though Tyrion might have some adventures somewhere).
Joffrey won't be a source of conflict like he was in Hear Me Roar-because there is nobody around for him to actually use to cause trouble. Tywin's vassals obey him, not his grandson. The boy king without a throne.
He probably gets packed off to the maesters or otherwise marginalized-as losing his kingdom and birthright for a world of primitives and savages is likely going to leave him agitated and angry. But he's just Tywin's grandson here. So maybe he will get scared straight or beaten into obedience.
Generally in Hear Me Roar style ISOTs(that is scenarios where the Lannisters and Westermen are ISOTed out of Westeros into some other world)-the "Baratheon" children are basically superfluous or are political pawns depending on the exact context. As without the Iron Throne, their just Cersei's kids. Their not heirs of the Rock, and don't really advance Tywin's ambition or secure his legacy.