The legal standard is whether the shooter feared for his life. It’s why there is almost never a conviction in police shooting cases. The suspect was either waving something around or posed a threat of some kind. In this case, La’an saw a Gorn looming over her friend, knew from prior experience that the Gorn kill and eat people, and shot to kill. Whether she shifted the phaser setting or had it already set to kill, the shooting would likely be cleared and ruled justifiable by a review board. I’m sure she will have a second or third thought after she learns the circumstances, but would still do the same thing again in the same set of circumstances.
This is dialogue from Hegemony.
La'An: I'd like them dead as much, if not more, than the rest of you. But that's not enough. We don't know what we're walking into down there. Phasers might not be enough.
Pike: I have something that might help. Pike to transporter, Chief Jay, is in-ship transport still functional?
Jay ( over comm ): Yes, Captain.
Pike: Could you transport crate 32 directly to ready room, please? Authorization Pike epsilon C-6.
Jay (over comm): Acknowledged, Captain. Transporting.
Pike: Ever since the Gorn started massing on the edge of Federation space, Starfleet's been working on weapons to counter them. Now all our ships carry these, in case.
La’An: "Gorn Protocols. To be distributed upon an encounter with the hostile species."
Ortegas: "Break in case of Gorn"?
Spock: "Phaser harmonics adjustments. To better counter their defenses. Scanner re-calibrations."
Sam: Last time, our tricorders couldn't detect Gorn at all.
Pike:Now they do.
They aren’t lobbing nitrogen hand grenades at Ortegas’s friend, but they can detect Gorn, they have re-calibrated phasers for Gorn, and there is a protocol in place that addresses what to do in any encounter with this “hostile species.” At a guess, that protocol is shoot to kill. Ortegas knew as much too.