You're mistaken in how unstoppable works.
Unstoppable prevents CC from afflicting you during the duration of your ability's usage (or the time you're unstoppable). It does NOT make you immune to CC.
So: Lux Q's you, you can still move with W unstoppable despite being rooted. However once your W finishes, if there's time remaining on Lux's Q root, you will be rooted for the remainder of that time since you are no longer unstoppable.
Unstoppable is HUGELY useful for displacements, as it makes them entirely useless. E.g. using your W as an Alistar is about you W you would make his W do nothing (except damage). However against stuns/roots/snares it only helps you to move slightly during the snare, it doesn't make you 'avoid' it.