I noticed that the reasons I like Lux in a team is because of all the utility. The stuns and slows can keep a highly mobile, high priority target (Zed, Akali, Yi) locked down enough for my allies to burst them in teamfights. Since the shield can theoretically get applied 10 times per cast (twice on each of the 5 members on my team, if we all get stuck in an MF ult, and I cast it just as it starts, for example), it probably as the most total damage negation of just about any shield ability. In lane, I've noticed that a lot of the damage I do is by getting a good combos with auto's in-between to trigger the passive as much as possible.
What I see from all this is a lack of reliance on AP. I don't believe the passive scales with AP (correct me if I'm wrong tho! SEE EDIT), nor do the CC affects (the binds don't last any longer with AP, and I'm assuming that I don't need the damage upfront when the bind hits because my team is going to turn and focus and burst whoever I catch).
So if I don't really need AP, what should I be building? CDR obviously, but you can get max CDR in 2 items. I'm toying with the idea of doing some AD and Attack speed items. I think there is a potential to do more total damage with my full combo that way, since a lot of my damage already relies on hitting auto attacks. Runnan's Hurricane applies on hit affects correct? So would it let me trigger my passive on 3 targets with 1 auto (if I mark at least 3 targets with a W or Ult)?
Could this be a thing? Has anyone tried it? Any other thoughts / is there anything I'm forgetting to consider?
EDIT: There has been some recent activity regarding the changes in the last patch (4.13), which nerfed the base damage of her passive and added 20% AP scaling. I feel this single change is significant enough to encourage an all AP build over a mixed damage build.