The degree of horror involved in Valerian’s execution depends on the source, but all agree that Emperor Valerian never left Persian territory alive.So, much of speculation and at least two forms of execution copied in Game of Thrones, but nothing known for sure.[snipped various speculations on exile, being forced to ingest molten gold and being flayed alive]
Despite not knowing exactly how Emperor Valerian died in 260 CE,
I never thought about it but you are correct about Game of Thrones. And speculation and history like this is sketchy. Lot of propaganda. Need multiple sources to make any sense. That is the thing about history, you can only draw framework conclusions. But even with mythology, there is usually a root of truth inside it.
GoT borrowed heavily from history for gruesome and ironic deaths. The death of Tywin Lannister (shot to death by a crossbow while sitting in the privy) was said to be similar to that of an anglo-saxon king.
CC