Scourge of the Throne's ability has an intervening "if" clause. It must be attacking the player with the most life or tied with the most life both when it's declared as an attacker and as it starts to resolve for it to have any effect. If, at either time, the player isn't the one with the most life or tied for the most life, the ability will have no effect. Notably, this is different than how dethrone works. (Dethrone checks only once to see if the ability triggers.)