I chose these runes because this will give Lux some pretty heavy power at the start of the match. Given her range, this will make it easier for you to overcome your enemy.

The way the items progress is since you'll be relying on the runes and the Doran's ring for power and health early on, you can use the Sorcerer's Shoes to penetrate the resistance most champions have and easily get a leg up on them.

Going into the Lich's Bane first is good because it gives you ability resistance, speed, mana, and the ability to do extra damage whenever you cast a spell. You'll need these to take down turrets early game and keep your opponents from catching up.

Then getting Nashor's Tooth to increase your basic attack speed and reducing your cooldowns by 25% is a must, because the faster you can cast your spells the more damage you can do with Lich's Bane.

By this point you'll probably want to buy Rylai's Crystal Scepter for the health just in case people start to focus target you to try and get easy kills.

Will of the Ancients to give your supporting team an AP boost, and the Spell Vamp will also help in coordination with the Crystal Scepter.

Finally getting the Deathcap if the match lasts that long to just utterly destroy your opponents.

However, if the opponents are building up too much spell resistance, then instead of Will of the Ancients get the Void Staff

Lux's very good at harassing so you'll want to max out Lucent Singularity quickly while dragging along Light Binding. Singularity is going to be your primary damage function, and you're going to only use Light Binding when you need to stun and finish off with Finales Funkeln, or use Light Binding in team fights.

Taking prismatic barrier even for support isn't very helpful because if you take it early on then you're leaving yourself vulnerable to a lot of the damage that Lux can deal out, and late game the shield doesn't do much in ways of protecting your allies.