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Hope this is better. Leave comments so i can adjust the content and make a nice build.
Lacking some survivablity, MPen.
This would fail late horribly.
I would rather say; set up a own build with voidstaff in it..
Let me explain.
With your Manapool and your Rabbadons you'l get 585 AP from the Archangels passive. Together with your the base AP and AP of rabadons you'll get 585 + ((140 + 45 * 4) + ((140 + 45 * 4) * 0,3))=1001 AP +37,791 Rune AP =1038,791AP.
The formula for magical damaage is
(AP*APratio+flat damage)*100/(100+(x-MrP)*(1-%MrP/100)) this would make
(1038.791*0.75+500)*100/(100+(x-8.55)*(1-15/100)) for your Ultimate.
If you would change your build from 4 ARchangels to 3 Archangels+Voidstaff you would get 901,55A. UUU less damage you think?. Then you are wrong. With your Masteries and Voidstaff you would have 49% MrPen.
You would do more damage with a Voidstaff past the 38 Mr mark. And every good player would get a negatron mantle if he saw a lux with 900AP. Let's they would go standard with a banshee's. It offers 50 Mr. Together with the basic 30 Mr you would get 80 Mr. So you would do, if you take the time a calculate it, 66.25 more damage. You will do more damage with Voidstaff in ALL your spells and it is cheaper than another Archangels.
So even if we would not take a deeper look in your build, you have absolutly ZERO survivability. Sry, but if a wild Udyr with Quicksilver Sash appears you are deadmeat on the ground. I will downvote this, because it's not the way you should play a caster. Also Lux is an Support/caster so this is even more fail. AP nuke yes, but a dead nuke does ZERO damage.