There's literally no reason not to. It depends how you read Starfleet, I suppose, but in my impression of Star Trek, a Starfleet officer should always act non-lethally unless literally no alternative is given. Stunning the Gorn versus killing it makes no difference to the mission, which is to retrieve Ortegas.
It's also insane to lethally shoot something that she vaguely thinks might be a Gorn when she has no idea where in space she is or what's going on on the planet, and thus what appears to be a Gorn could be literally any reptilian species (in the same way that Betazoids, Bajorans, Ilyrians, and Humans all look virtually identical, especially at a distance in low lighting and wearing face-obscuring clothing, as the Gorn was).
And even if the script does intend her to fatally shoot it because she IDs it as a Gorn, the portrayal on-screen just makes it appear that she had her phaser set to kill by default (on a rescue mission in the dark!) and fired instantly at a vague cloaked figure.
I think a snag to this theory is that the entire security team had their rifles set to kill. La'an never gave an order to switch to kill (nor did Chong appear to be directed to act anything with the rifle prop that would suggest doing so), all three of them just fired simultaneously, all already set to kill.