She's not 'missing emotions', she's been stuck in a horrible hellhole for ten thousand years and is, to be light, poorly socialized. There has never been a moment where she appears to completely lack emotions, she just lacks expression of those emotions and a lack of experience with and understanding of things we generally associate with those emotions. She has a full range of emotions, she's just been deadened to a lot of the negative through overexposure and is unused to the positive due to underexposure, so she's coming from a fundamentally different road.
While she's not autistic (and I caution to never treat her as if she is), it's a similar situation you see with people on that spectrum; it's not that she doesn't have emotions, it's that she's not expressing it in the ways you're typically used to seeing.
And god damn I hope Golbez isn't some fragment of another person in any way. Let him be his own person! God knows that of any FF reference character, it's Golbez that deserves that respect.