Lux is a great champion and for that she need the right runes to make the difference in game with lack of mana so for runes you pick
greater mark of insight 9 x 0.95 = 8,55 ( magic penetration ) = 9x410 ip = 3690 ip
quintessence of potency 3 x 4,95 = 14,85 ( ability power ) = 3x1025 ip = 3075 ip
greater glyph of potency 9 x 0.99 = 8,91 ( ability power ) = 9x410 ip = 3690 ip
greater seal of replenishment 9 x 0,41 = 3,69 ( mana regen / 5sec ) = 9x205ip= 1845 ip

I always play Lux as mid and not on lane even if in team is other AP champ that's fits for mid
In the beginning you go to take the Mana Buff so for that you need to ask your teammates to help you
As you get the mana buff you go immediatly mid and start spam your E skill ( Lucent Singularity ) at your enemy. At level 2 you learn Light Binding ( Q = stun skill ) and try to catch your enemy with then atack with E . for sure that will angry you enemy trying to kill you or run away
I always learn E all the time I can and Q , I let W for end game.
Till level 6 your Mana Buff will finish and for that you have Clarity ( dont let your enemy go base ). Your enemy should have their hp around 50% or lower when you reach lvl 6
As you reach level 6 and their hp is around 50% or lower you learn immediatly your ultimate (R=Finales Funkeln) and catch them with Q then you Ignite them send an E + R so it should look like that : Q + Ignite + E + R ( you must do that verry fast ) that will mean you will have your kill granted
You keep doing that and you will have a nice score with 0 Deaths
When you try to gang always be sure you wont MISS your Q skill then sending E + R
When you try to escape from a gang 2vs1 , 3vs1 ... your Q is your PROTECTOR Angel ( can stun 2 enemys ) so be sure you wont MISS , if you miss try to run to nearest teammate ( as you reach your destination use your Q ) then try to turn them back or kill them
When I'm with my teammates I allways stay behind them , support them with Q , attacking with E and R all the time cause of it's 24sec cooldown

I start play the game with the following Items :
2x Doran's Rings
Ionian Boots of Lucidity
Rabadon's Deathcap
Morello's Evil Tome
Deathfire Grasp
Void Staff
Lich Bane

In the late game I sell 2x Doran's Rings
allways use your skills and Deathfire Grasp skill
You will have your Ultimate skill ( R ) in 24 seconds or lower
After all cd is all about and AP
Hope this help all players of Lux
This is also my first build . Enjoy it !!!

In the Summoner's Rift 3v3 Lux can solo also
If u think you cant sollo then you go bottom lane and keep farming with your E Skill and do some dmg to enemys with
In 3v3 the items wont change to much but there people will get magic resist against you so that's bad for your magic Penetration and ultimate
try to gang as much as possible all the time .
Be more like a jungler changing lanes : top-bottom , bottom-top
So the first items we will buy there will be :

2x Doran's Ring
Boots
Ionian Boots Of Lucidity
Abyssal Scepter ( cause of it's magic resistance and reducing the magic resistance of enemy champions . in every 3 vs 3 you meet an AP so you need some magic resistance too )
Void Staff ( is all about it )
Deathfire Grasp ( cause of it's cd's reduction and active spell that's deal damage )
Rabadon's Deathcap ( before of getting Rabadon you lack ability power )
Haunting Guise ( the last item you will get )
sell Doran's Rings to make space in inventory for the last items
If you see the things are not going well sell the Haunting Guise and get Lich Bane
If your team is not going well and the enemy team have a feeded DPS get Thormail so you will survive longer or Frozen Heart depends if there is an dps-atack speed ( this will be verry usefull cause of it 20% cd's reduction and slowing enemys with atack speed ) and forget about the Lich Bane

As Playing against Lux with other champions or Lux always try to hit it fast and run out of it's Lucent Singularity range.
Dont let her stun you cause this will mean you will lose about 15-30-35% of your current health depends of his Ability Power and Magic Penetration
Always try to get magic resistance and make her miss his Q
When she miss his Q go fast and attacker her (that's mean about 7 seconds or lower ) , his Lucent Singularity wont hurt you so much
When your hp is bellow 50-30% dont let her hit you with his ultimate always run like crazy :D change everytime your possition
You can play againt Lux with Champions with long Range or Champions that have A.O.E Damage
When you try to gang with your team and she is near and Support his team make all the possible to kill her so his team will lose the Support and they will not counter-attack and that will mean free kills
If you are being hit by Lux stun ( Light Binding ) use your Flash if you have and you may have a chance to survive
Always try go get both mana buffs in 5v5 so she wont have so much mana and mana regeneration and that means she cannot support all the time with stun/lucent
When you are at Baron and you encounter the enemy team dont let her hit you and dont let her steal the Baron she is your primary Target cause the others from her team will be busy to kill you but if you kill ther they all gonna die and SCREAM !