MTG reacting instant speed on creature entering game
This has to do with priority. When anything goes on the stack (a spell being cast, a trigger from anything etc), players get &quot;priority&quot; (a word to describe the chance to do something) in APNAP order (active player, non-active player).
When a creature enters the battlefield and has a triggered ability that triggers when it enters the battlefield, that trigger goes on the stack and then all players get priority before it resolves. When a creature does not have such an ability, then the active players gets priority until they either pass actively (such as &quot;moving to end step&quot;) or cast/activate something else.
To go into your example, they have a moment with Lurrus on the battlefield where they have priority (i.e. you cannot cast/activate something) and they can for example cast a creature from their graveyard. Only when they do this, you get priority and can then kill Lurrus in response.