This guide is for different play styles for Lux:
-The classic AP Mid (that I love ;) )
-Support Lux, it is also very fun to play her like this, be warned you start as a support but you switch late game to a AP carry.

Their are many ways to play Lux, and the items I propose are the ones i play with when I'm with Lux, they offer a good balance between AP, CDR, and survivability. In late game you have about 21secs of CD on your Ulti not bad if you ask me ;)

As I already said, there is many ways to play Lux you don't have to agree with my build, it's the one I like and use.

Pros:
-Great farmer
-Very good harras in lanning phase
-Very good range
-Very fun to play with :)
-2 ccs, a cage and a slow
-Her shield scales well and is very useful anytime sice unlike Morgana's it's not limited to magic damage

Cons:
-Squichy champ early game (does NOT like getting ganked)
-Item dependant
-Your team might say your Ksing (even if it's not true)

In mid: Harras as MUCH as possible, use your cage then auto-attack to use your passive then your E and auto-attack again, in early game you can take out (depending on the champ your up against) 1/2 of their life.
Be careful about ganks you are very squichy early game, if you are too squichy go for Rylai's right after boots, or at least get the belt...

As support, help your Adc by all means available its better if you die and they live for exemple... use your E as a ward in the bushes (still ward the river for ganks), don't be afraid to use your abilities, you got clarity.

You can sume it up in a few words:

BEEEEEAAAAAMMMMM thn BEEEEAAAAAAM and BEEEEEEAAAAAAAMMMMM again :D