Can Immortal Phoenix revive from Cull the Weak in these two scenarios?

Scenario 1: I control Immortal Phoenix and my opponent controls Lucian. I cast Cull the Weak targeting my own Immortal Phoenix — can I revive it from that? Scenario 2: I control no units but have Immortal Phoenix in my trash while my opponent controls Lucian. I cast Cull the Weak, kill none of my own units, and my opponent is forced to kill their Lucian — does Immortal Phoenix trigger from my opponent killing their own unit?