Hi all.

First Things First:
YES: It is possible to get 1K AP with Lux. With this build complete, all your pots, and 20 stacks on your Mejai's. You will have 998 AP (Yes, technically its not 1000, but 1K sounds better than 998, so deal with it). Having said that:

Welcome to my Lux Carry Build, please enjoy...

This is my second build and it happens to be with my second favorite champ: Lux. She can be incredibly useful in each stage of a game. She has a double snare, a slow/AoE Damage, a Shield that can hit every member of your team twice on each cast, and last but not least the Laser, which is what really makes Lux fun to play.

Proper Spell Rotation:
What you want to do is combo your spells beginning with Q, throw your E, follow with your R, and detonate your E after using your laser. This will ensure maximum damage is being dealt.

Passive:
This is the biggest difference between a good Lux player and a bad one: Proc'ing your passive is essential to playing Lux well, especially after you have a Lich Bane. Lux's passive, for those who don't know, deals between 20-190 magic damage, depending on her level. It can be used on enemies with the glowing refracted light that appears on an enemy Lux has used a spell on. Try to proc your passive as many times as you can without taking too much risk.

Team Fights:
Your role in team fights is to snare enemies with the highest damage output, preferably melee champs, throw your shield on as many allies as possible (remember it can hit twice), use your AoE to hit as many champs as you can. Use your laser to hit as many champs as you can while making sure you hit carries/casters, as they are the ones you can really hurt.

Proper Laser Usage:
When you have your rune page complete, as well as blue buff, you will be able to use your Ult every 18 seconds or so. So don't be stingy with your laser. I like to open team fights with them, and usually by the time its back up I can use it again to pick off fleeing low-health enemies.

Creep Farming: Lux's auto attack is mostly useless without her passive, it works fine in the early game, but once you have enough mana to throw some spells around you shouldn't be afraid to use any of your abilities to help you farm (even your laser). This build takes a lot of money to finish and you will need to farm a good deal of minions to finish it. In games that went over 40 minutes I nearly always have over 200 creep kills and have been over 300 quite a few times.

How to know if you should be getting Mejai's:
I get Mejai's nearly every game. The only circumstances in which I do not get Mejai's are if I am doing so poorly I cannot put it to use. Additionally, if I die too many times late game and lose a majority of my stacks, I may sell it for either a Deathfire Grasp or a Void Staff.

Elixir of Brilliance:
The EoB is one of the best items in the game, it also only last a few minutes. When you go back to buy, if you have enough money left over, you should always buy one from mid-game onward, it is absolutely worth it.

Some Lux players favor magic penetration in their runes, I favor cooldown reduction for this reason:

You don't always need magic penetration, but cooldown reduction is always useful. In addition to this, magic penetration items are much easier to get and fit better into Lux's ideal builds. Remember that cooldown reduction caps at 40%, this build is going to have you sitting around 30-35 CDR. If you can make it to, and can sustain, 20 stacks, sell your Ionian Boots for Sorc Shoes. The remaining ten percent can be made up with the Elixir of Brilliance or Blue Buff.

If three or more enemies are starting to get a lot of magic resist, or if i notice I'm not hurting them as much as I'd like, I will get a Void Staff instead of a Zhonya's Hourglass. This will force me to be more cautious when I use my auto-attack's to proc both my passive and Lich Bane's, but I will be able to do significantly more damage. After you have her mastered you will be able to play far enough back to keep your stacks and get massive AP.

Obviously Flash and Ghost are the spells you want for Lux, this ensures maximum survivability. If you find yourself wanting clarity you are spamming you spells too much early game and/or not getting enough blue buffs. Lux thrives on blue buffs, and you should have it as many times as possible all game long.

As I said with attacking enemy champs, it is absolutely vital that you are using your passive to help you kill creeps. Your can hit four attacks before the luminosity fades if you are fast enough. This build is very expensive, you will need to be well over 200 CS if you intend to finish it. Learn to use your passive well and you will thrive.

In team fights, you role is to snare the enemies with the highest damage output, AoE where it will hurt most, and Laser weaklings or groups.

Lux has fairly long range, try to cast your spells from as far away from danger as possible in order to ensure your survival and maintain your stacks. The bonus AP is great, but 20 stacks is so much better than 19 for Lux because of the added CDR.

Use your AoE to slow enemies but blow it right before they get out of the radius.

Try to do your full rotation on the one of the other team's carries. If you have a your Lich Bane they are guaranteed to die if you follow the Q - Throw E - Auto Attack - R - Detonate E - Auto Attack. Landing this full rotation takes three or four seconds even when you're really fast so makes sure you're going to be okay before you go in. If you get focused, you will likely die before you finish your rotation.

Lux will automatically Auto Attack whoever you throw a spell at, so you dont have to worry about clicking them, just learn the timing so she gets her attacks away between her spells.

Pros:
-Great Damage Output
-Several CC's
-Shield for Teammates and Self
-SHE HAS AN EM EFFING LASER!

Cons:
-Squishy
-Mostly have to Stun & Run when up against Tanks
-Bad Pusher (However you can use a spell on a creep and then use the proc from your Lich Bane to do a lot of damage to structures)