As Lux you are going to be a high damage dealing low cooldown squishy but powerful easy escape champion.
As some people use Lux as support, I think that is such BS.
Why use such an amazing mid champion as a support, when you could play someone likeTaric, or Leona.
Anyway, I will have chapters explaining the pure power of this build.

In my Runes I like to go strong and defensive.
For Marks take Magic Penetration so that you can counter and Magic Resist, and Maximize damage.
For Seals take Ability Power so that you can have some good AP to start.
For Glyphs take Magic Resist so that you can take at least some damage, combined with your shield, encounters will go your way.
For Quintessences take 2 Ability Power Quintessences so that you can increase offensive power.
Also, take 1 Cooldown Reduction Quintessence so that wth the Morellonicom, Athenes Unholy Grail, Masteries, and this Rune, you will have the full 40% CDR.

For Masteries look above as it will be worthless looking at them and reading this as well.

As well as my Masteries guide, look above because it would be worthless to look at both the build, and this.
Cooldown Reduction and her pa***ive are taken into account in this build.

To farm I recommend sending Lucent Singularity to their Caster minions, and then manipulating your passive to last hit them all.
Meanwhile, last hit any of the Fighter minions that get low enough.

For the spell,s look above, but I still still explain why.
Lux is not tanky, at all.
That is why you can take a defensive spell like Barrier or Heal.
Even though I don't recommend them.
so I would say get Flash and Ignite, as she usually bring you to nothing but can't finish you off as she is rather Mana hungry.
And even though she is Mana hungry, DO NOT GET CLARITY!
That is a huge mistake many people make, the build above will keep your Mana up fine, and if your Jungler has any brains, he will give you blue quite often.

Her passive is something people do not take into account.
After using an ability, say Light BindingL, throw your Lucent Singularity but do not activate it immediately, as you want increased damage of course.
After an ability she does extra damage on her next basic attack, that is why some people get a Trinity Force.(Sheen Passive)
But Use Light Binding into Lucent singularity, but before activating Lucent Singularity use a basic attack.
Then you should activate Lucent Singularity and basic attack once more. You have a huge advantage now.
Ignite them and then use Final Spark. Then try to basic attack once more.
Before level 6 just ignore the Ult of course. But low cooldowns should help get it back after level 6.

Pros
Passive
Good Snare
High Damage
Amazing Ult
Low Cooldown Ult
Easy Farmer
Good Shield
Cons
Mana Hungry
Mana Hungry
Mana Hungry
Mana Hungry
No Great Escape

I can't stress how Mana hungry she is.
But in this build you will have crazy low Cooldowns, high damage output, Amazing Shields, No Mana Problems, and have a GREAT time.
Enjoy wrecking as the champion they never see coming.

P.S. Her Final Spark will be near a 20 second cooldown, less than Ashes Hawkshot.