Hierarchy of dying - Is this Venn Diagram accuarate/complete
The new rules changed for innistrad. Dies and Enters the Graveyard are now very similar (A creature “dies” if it is put into a graveyard from the battlefield; rule 700.4.). Dies now means "is put into a graveyard from the battlefield.” So I'd start by putting "dies" and "is put into graveyard" together.

Toughness - Damage &lt; = 0 makes little sense in that context (because it is completely arbitrary and has no in game analogue). 

I'd just keep sacrificed, destroyed and 0 toughness as 3 entities inside "Died", with lethal damage inside destroyed, (and also add deathstrike inside destroyed). 

Make the wording shorter too, it's obvious in context that lethal damage inside destroyed means it was destroyed by lethal damage. No need to say "dealt lethal damage".

Edited: Deathtouch as a subset of death touch. Legend Rule as another way to Die / put creature in graveyard.


  Left Battlefield
  
  
    Exiled
    
    Died / Put into Graveyard
    
    
      Sacrificed
      
      Legend Rule (like Diego noted)
      
      0 Toughness
      
      Destroyed
      
      
        Lethal Damage
        
        
          Deathtouch (as Hackworth noted, Death Strike causes lethal damage)