Well, looks like everyone has their own idea of how to build Lux best. What a wonderfully flexible character.

Start with meki
make into tear, you leave it at tear till end
mejais
sorc or lucidity
deathcap
morello's
RoA
Lichbane
Archangel upgraded..

In all honesty, I think building lux with Cooldown reduction/MP in mind is best. She doesn't scale fantastically with AP, so having a way to cut through your enemies defenses, particularly early game, can net you kills and eventually lead to you getting more and mroe as you farm. Mind you, smart foes will counter this, but most people tend to not be so smart.

A build for good early, mid and late game:

dorans ring
meki + pots

tear
(any order)
sorc shoes
mejaj
fiendish codex

Then: morello's, deathcap, archangel
After that you can sell the ring for something like a void staff.

yes i know i buy no survivability. That's because I abuse the fact that all Lux's spells are 1000+ range.

Magic Penetration is #1, CDR to Cap should happen with elixir/blue neut buff(unreliable but happens), and AP is last. I don't personally have mana issues with Lux. I use support masteries 9/0/21 with Teleport and Flash generally, since lux's ult is all about positioning flash comes in handy as an escape or to get the right angle to hit your enemy's whole team. Mejais should only be used in a pubstomp/game you question whether it's ranked or not it's that easy. Even in those kinds of games mejais will do nothing but overkill, it's generally safer to go Void Staff instead. I like the sheen idea but my general build is RoA/Sorcerer's/(Deathcap or Void Staff, 3rd and 4th)/Usually the game ends by this point if not grab Lich Bane and/or a Defensive item. It varies around the 3rd-4th item heavily based on what you need. Defensive, Support, or Offensive. Some games I find myself getting Stark's, some the spell vamp book, it all depends. I use Penetration/CDR/MP5 and flat AP Quints. I have around an 80% winrate with lux and I've only been negative one game.

i like
dring
sorc boots
soulstealer
rabadons
zyonga

but i run cdr blue so cdr boots are better if you have ap blue

this build is ideal though i think
http://www.solomid.net/guides.php?g=441

I'd suggest to drop AA from your build, it's not really worth it.

The core items on Lux to me are Sorc Shoes and Deathcap. She's a burst AP, and this will give you that burst. As long as those 2 things are in your build you're on the right track.

Items to get besides that would be:
-Void Staff - if they stack MR
-Banshee's - if you need survivability
-Deathfire Grasp - Another spell, AP, and CDR
-Morello - CDR + AP
-Lichbane - Roll over towers and more burst


What I've been doing lately is starting with:
Regen Pendant + HP pot
-Philosopher Stone & T1 Boots
-Another Philosopher Stone & Sorc Boots
-NLR
-Blasting
-Deathcap

Usually get a deathcap at about 20-26 min

I think you should definitely max cdr on Lux, but how you do it is totally up to you. If you're ap carry, you can blue buff + blue elixer to take care of the majority. If you're support, you probably won't get that blue buff. I take flat cdr blue's and quints, 9/0/21 masteries. That's just shy of 20%cdr, so building the other 20% isn't too tough.

Ap vs magic resist also depends on your role. If you are trying to carry, I think void staff + 15% mpen mastery is usually enough mpen. Then I build heavy ap. Deathcap + archangels + void staff is a ton of ap, and your nukes will hurt everyone. If the game goes long enough, a lichbane on top of this will give you outrageous damage.

If you're support, you can even ditch ap for auras if you really want, although I think most of us laser snipers still like the ap. Either way, I prefer to use lux's range to kite/harass. It's not uncommon that I can take a squishy carry out of the fight with a pair of lasers before the teams even engage, but that's just my playstyle.

I've been maining Lux in ranked games for sometime now (with a 76% win ratio), here is the lux guide i follow.

You do not need AA ever on Lux.