Letting the elementals fight alone is a neutral act (acting principally for one's own benefit), unless you promised to help them, or suggested fighting the gargoyles together, then it's an evil act (cruelty, acting specifically to harm others). The text "let them work for their freedom" suggests Lawful. So LE seems like the right choice, though it could just as easily be LN, TN or NE, depending on other factors.
As for the fighting alongside the elementals, clearly that's a good act because your character says "we won't abandon them!" that's acting for the good of the elementals. One could argue that fighting alongside them would increase the changes of victory (neutral act) but the dialogue doesn't suggest that so whatever.
The problem here is that refusing to abandon one's comrades is quite clearly a lawful act, because it's sticking to one's moral code, or perhaps the law of the land - one doesn't abandon one's allies in battle. Owlcat seem to be going for a 'logic = lawful, impulsive = chaotic' thing here, as InD_ImaginE says, but alignment isn't always that simple in my opinion - sometimes that fits, but it feels awkward here. Standing up for what's right, even if you are passionate about it, that's not necessarily chaotic.
A more obvious chaotic action would be agreeing to Kanerah's plan and then changing your mind when you saw them fighting, or vice versa.
I think these alignment shifts would be a lot easier if Owlcat focused on one axis at a time instead of trying to do both. This scenario is clearly primarily about good vs evil, introducing chaos/law into it just makes it a whole other can of worms.