People aren't questioning that she fired, but rather why the writers chose to have the entire security team's phasers set to kill. Obviously La'an panic-firing wouldn't have mattered if the phasers were on stun, as is often shown to be standard procedure (and this mission is a textbook example of why).
The answer is that the writers really wanted the Gorn to die by La'an's hand because a) it's a dramatic ending and b) so the Metron could sneer at humans for being violent and thus get the "we hope somebody passes our test in the future, wink wink" reference to Arena in there.