Before reading this build, sorry about my grammar and my conjugation, my main lenguage is the spanish and i tried to translate it as good as i can..
For some reason i can't link mi lol account to the mobafire account. I main MID, I'm Platinum V in LAS (Latin America South) My summoner name is raami96.
Lux is an AP carry, she's very usefull for the team, becouse of her incredible magic damage. Her meta is the MID lane, she can also be used as supp but I will explain you how to use it in MID.
If you're looking for doing a lot of magic, Lux is the one for doing that, her combo can finish the adc in just seconds, securing the teamfight.

I'll put here a list of Pros and Cons to know more about Lux:

Pros:
- She got a good early game, you can make some kills even before Lv. 6.
- Her ultimate has a long range, it can secure kills or steal them. :)
- In late game she's very usefull for the team.
- She can farm with her e (Lucent Singularity).

Cons:
- She is very squishy.
- If she is ganked, she will die very quick.
- For doing her combo is almost completely necesary to hit her Q.
- She can be countered so hard, with champs like Fizz.

Weak against:
1º2º3º4º 5º
Strong against:
1º2º3º

It's essential in lux. You'll use it to get closer to the target and land your Q, or as always, to run like a B***h when you see your screwed.
If you want to play offensive with lux, ignite is the best choice to do it. Personally I use it very often.
Barrier, as a MID LANER, is not a bad option to play defensive.

LIGHT BINDING (Q)The snare, it puts the enemies in a "prision", it doesnt stun, just inmovilize the first 2 targets in line. It's the first step to land your entire combo and doing tons of damage.
PRISMATIC BARRIER (W)It's a very usefull shield. In the lane phase you can use it to counter an ignite. In late game it gives an big shield to the tank or save the life of the adc
LUCENT SINGULARITY (E) It's a circular spell, that can be reactivated, when it explodes it does a hugh amount of damage, it's ideal to land after the Q. It also work perfectly to farm or push fast.
FINAL SPARK (R) It's a powerfull spell, it goes in in one way and it have a very long range. It can be used to secure a kill. The best way to use it's landing your Q, sending your E, using your R and reactivating E. In late game you can also use it to farm a wave of minions, with the items of CDR you'll have it back in 30 sec.

The ideal masteries for lux are the showed before (21-0-9), but a 21-9-0 is also viable. I personally use the 21-0-9.

QUINTS
x3 The AP Quints are the best choice for lux
x3 The Magic penetration ones are viable to but i don't recomend them


MARKS
x9 The Magic Penetration are the most usefull.
If you have your Quints of Magic Pen. use the AP Marks


SEALS
x9. I always use the seals of armor.
x9 or x9. In the case that the enemy team have a lot of ap (AP jungler, AP top), use AP or Mana regen seals.


GLYPHS
x9 The normal ones are the magic resist glyphs
x9 x9. If the enemy team doesn't have AP champs you can use glyphs of AP or Mana regen.
x9 If the enemy team has an AD mid but an AP top or Jung use the MR p/level glyphs

Early Game
Well, being a Lux in MID, it's very important to buy it, it offers vision in one of the sides of your lane to avoid being ganked. In late game you can change it for the red trinket if your team needs it.
The Doran's ring is a very good item to start a normal game, it gives you Ap, Hp and mana regen, sometimes when you doesn't have inoff money to buy the items that you need, buy one more of this if you want.
If you want to play very defensive, buy it with potions and a ward, it's a good choice when you enemy have a Mid and a Jungler with so much damage (For example: Fizz and Elise)
When the enemy has a AD mid like Zed, it's a good idea buy this, becouse it allows you to buy the seeker really quick.
This item it's very important in the first back it gives you a lot of Mana regen and also gives magic resist. Try to back when you have the gold to buy this item, or another doran's ring and later this.
It's very important to rush it when your enemy MID is an AD MID. If you're against a Kha'zix you don't have to finish it. But if you're against a Zed rush Zhonya's to counter his ult. In both situations buy a mana regen item, Lux really needs it.
It's a really good item it's cheap and y gives you a lot of mana. If you bought Seeker's you should buy one of this. You doesn't have to finish it, you can buy other items like Rabadon. In cases of wanting only AP and nothing of Magic Resist. If you're against Rize it's a good choice.
In MID is VERY VERY important to buy this, buy one in every back if you can. This little things give you inoff vision to save your ***, giving you vision arround your lane.

CORE ITEMS:
Bueno, este es el item principal para Lux, debido que le da mucho AP plano y Lux realmente lo necesita.
Estas botas, son las que se compran siempre con Lux, por tener Magic Penetration, es muy importante. Solo hay raros casos en los que se tiene un mid muy difícil que los tiene bastante acorralados y es necesario contra arrestarlos más, pero insisto, no es muy necesario, comprarse botas de armor o magic resist.
Bien, El void staff, pienso que sea la build que se obtenga, defensiva, ofensiva, es muy necesario para Lux porque la ayuda a sacar daño y no la hace useless, debido a su pasiva.
El Zhonya's es un item muy importante para lux, casi tan fundamental como los anteriores nombrados, ya que al ser un AP CARRY, es muy necesario tener algun item defensivo para el late game, no es muy recomendado comprarlo antes de los otros items que mencioné, pero como explique antes hay algunos casos en los que se necesita hacerlo.

Situacional
Hay que comprarlo en Early Game. Bien, hay veces en los que se tubo un early game con "suerte" y obtuvimos muchas kills, o en los que el team tiene mucho front line y no es tan necesario jugar defensivo, que no estaría mal comprarse el Mejai's ya que es una Buena opción OFENSIVA. (Es un item que recomiendo personalmente comprarselo una vez que hayamos dominado por completo a Lux y no cuando la estemos aprendiendo a usar debido a sus stacks y es una perdida importante de oro en early game).
El lich bane, es un item muy bueno que va muy bien junto con la pasiva de Lux, es una opción que recomiendo cuando tenemos mucho AP, ejemplo si tenemos un mejai's lleno, ya que por mas AP, mas funciona este item. Es una buena opcion OFENSIVA.
Bueno, el Deathfire, es otra buena opción OFENSIVA, se puede utilizar muy bien cuando se acerta la spell de la Q y se esta cerca, tirando su ACTIVA rapido y luego E R E para lograr más daño. Esta opción es la que comúnmente elijo con Lux.
Bien, hay casos en los que realmente como AP CARRY te hacen mucho focus, en estos casos, no estaría mal comprarse un GA, debido a que te sirve mucho para que el team se reacomode y tener nuevamente la oportunidad de planificar las cosas una vez muerto. Opción DEFENSIVA.

Bueno, como ya les dije, Lux es un AP CARRY con muy daño, para utilizarla es conveniente usarla en forma de POKE, sirve mucho, con los items de mana ya mencionados, estar spameando la Q y la E no es mala idea, incluso aveces la R. Hay que tener cuidado de no acercarse tanto cuando se pokea, porque acuerdense que son el AP CARRY y es MUY IMPORTANTE para ganar no morir rápido en las Team Fights.
En cuanto en la Lane Phase, Lux es un champ que puede fácilmente obtener kills si se juega ofensivo sobre todo si se juega con el summoner spell de ignite.
Sería lo adecuado en Early Game y Mid Lane, debes en cuanto pushear rapido la lane y tratar de rommear un poco a top o a bot, ya que de gankear con lux y acertar la Q, es una kill asegurada. Es importante tener cuidado cuando se rommea con Lux, ya que es un champ MUY FRÁGIL y puede morir facilmente.