The pit is not really a Al Ghul reference to the Lazarus pit. It is instead a reference to Peña Duro an Caribbean island prison where Bane was born in. Bane was born in Peña Duro since his father was a revolutionary who helped start a civil war in this Caribbean island. Since the victors of the war could not capture Bane's father they threw his girlfriend into the prison instead, she was pregnant with Bane at the time and gave birth to Bane inside the prison.