If Sower of Discord’s controller is dealt damage that causes them to lose the game at the same time that either of the chosen players is dealt damage, Sower of Discord’s triggered ability won’t resolve and the other chosen player won’t lose life.

Sower of Discord’s triggered ability causes the second player to lose life. This isn’t damage and it’s not caused by the source that dealt damage to the first player.

You must choose two different players. You can be one of those players.

If Sower of Discord is dealt lethal damage at the same time that one of the chosen players is dealt damage, its ability will cause the second player to lose life.