Zoe's ability's demonstration.

Well you can all see for yourself exactly whats what and what does what.

So yeah, shes a lich bane user, but shes honestly not all very busty, I'd still classify her as an AP assassin then a burst mage to be honest. Granted the Q can indeed do some damage, it takes a lot of planning and patience to really get the damage from it. Best used in combo with her Sleep bubble i think.