Tweaking some arts and skills (and actually giving Gwin skills lol) helped a bit, though I think what helped the most was that at the beginning of Lao's 2nd phase I was able to fire off a G2-Buster, which staggered him and allowed for a quick Bind that gave me the chance to deplete about a 1/3 of his health before he stole all my Skell fuel. Remembered to the kill the chimeras as quick as I could (there was 4 and not 2, though not all at once) too, and actually use the consumables I'd been saving up all this time. Eventually came down to me and Lin duking it out with him, and we managed to pull it off.
It did answer most of my questions (I was afraid for a while there it might not) and confirm the suspicions I had about some things (mainly Elma). I'm surprised they actually went and posed more questions in the scene after the credits (which I'm pretty sure is related to the 2 questions the game did not answer in chapter 12), I just
really hope that they are answered in the post-game somehow.
Also holy crap Elma looks a lot like v3 KOS-MOS