Scourge of the Throne

The +1/+1 counter is put on the creature before blockers are declared.

Once dethrone triggers, it doesn't matter what happens to the players' life totals before the ability resolves. You'll put a +1/+1 counter on the creature even if the defending player doesn't have the most life as the ability resolves.

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.)