This lux build focuses on damage
only use this build if your familiar with hit and run tactics.
stay at edges of team fights , cause when they get you your dead.
But if played well you can do some serious damage and help the whole team with stuns / shields.
use stun bom lazerspecial and an auto attack for loads of damage , then get out.
dont blow up the bom till special hits , bom slow helps hiting the enemy.
stun / bomslow / shield are great to escape enemy ganks. if all fails you still have flash

Lot of AP and some magic penetration for most damage

focuses on AP and damage output , with bit cd reduction

starting off with boots + hp pots to stay in lane long enough till you can buy tear godes , or atleast meki pendant. could swap some hp pots for mana pots if needed
once you have tear of godes mana problems will fade
next item , the moneydagger gives a bit ap and will help you build up the itemlist.
about 15min or so till the dager pays itself off, after that its pure profit
magic penetration boots for more damage
then i get to sheen , so tear of godess can build up more mana stacks before upgrading it
then finish archmage staff
you get a decend amount of ap by that time , time to buy a rabadon.
after that lich bane is exelent choise , couple autoattacks in a fight for huge damage
hourglass for more ap and bit protection , and finaly voidstaff for the much needed magic penetration.
sell the money dagger once you need room

maxing out singularity as soon as posible , sinse it will be your main harasment spell.
geting lvl 1 binding and barier as soon as posible aswel so you can use those abilities when needed. when you cant lvl singularity , lvl the barier , it will shield for huge amounts once you get some ap. Binding is maxed last