In Arrow, Ra's Al Ghul is killed by Arrow, whereas in Batman Begins Ra's is killed by Bruce Wayne. How can he be killed more than once and who killed Ra's Al Ghul first, Batman or Arrow? Is Malcom Merlyn from Arrow the Ra's Al Ghul killed by Batman in Batman Begins?
Ra's al Ghul is a Batman villain created in 1971. He has spanned multiple titles, and media. He's been killed, and resurrected multiple times (Lazarus Pit or otherwise). The Ra's al Ghul in the Nolan Batman Trilogy, like in the comics, is a person, NOT a title/mantle. The Ra's al Ghul in Arrow is simply the title of the leader of the League of Assasins. Neither universe overlaps, so neither "killed" him first. There is no connection between them.
but the Oscar-winning actor had to pass because he didn't have the time for The CW series. Mark Pedowitz, president of The CW, told BuzzFeed that the network reached out to Neeson, who played Ra's al Ghul in Christopher Nolan's Dark Knight trilogy. “We never thought he would,” said Pedowitz. “We quickly went to him, just on the off-chance that he had the time to do it.”
If you watch the crossover episode from Supergirl Season 1, which is The Flash come and said he come from another world. You can watch The Flash and listen the explanation by Cisco. Supergirl, Superman and Batman live in one world when The Flash, Green Arrow and Merlyn live in another world. The same earth in the different world. Both of that world had their own Ra's. For DC's superhero that don't have a superpower or supersuit (like ATOM), killing Ra's is a last proven to use "super" term.