Not Updated For Current Season
Lux may look like a dumb blond, but she is a deadly foes, particularly if yer up against her at mid. Only a few champs can hang with her mid, Vlad and Kennan being the strongest against. The key to Lux is mastering her combo. It's all about getting over a ranged attack immediately following your magic attacks. Lux's passive allows her to deal massive damage early.
Bad Lux's need Rod of Ages. She's squishy, but she has great range. If yer doing it right, you don't need to waste time on health and resistance items. Lich's and Frozen Heart provide the armor and magic resistance you need late game, while early game, you shouldn't be getting near enough to anyone to get killed, and if they do come near, as long as yer level 2, you can kill them. More on the combo later.
OK, I'm not gonna go over the items, masteries, etc. Lux should be all about AP and Sheen for the first half of the game. If you get bored, stack some attack speed increase items, like Nashor's Tooth. This allows Lux to get off her attacks faster to trigger her passive, which means you can hit your e, then ping off all the passive marked minions and champs quickly. I rarely do this, however.
The key to Lux is running her cycle. At level 2, you can stun, ranged attack, e, ranged attack and drop most champs to at least half health, if not lower. Always try to land a ranged attack on any champ you've marked with your passive. This is how you can drop your lane enemy below half health before you run your combo.
Use e to farm and hit champs when they come near to farm your minions, then hit them with ranged. If they're away from minions, snare them, then hit them with ranged attack. This is why I suggest getting shield early and getting sheen early: those two allow you to expand your combo quickly.
The combo takes some learning, though. First, snare. Then, immediately throw e underneath them. Hit them with a normal attack to trigger the passive from the snare q, then trigger e. This will give them another passive mark, which you should rip off them with another ranged attack. Finally, throw your shield to trigger sheen, and then hit them with ranged again. Boom, they should be near death.
Cooldown is also very important on Lux. With proper cooldown reduction, your R becomes part of your rotation. End your combo with R, then if they're still alive, hit them with another ranged attack.
This is the stuff that's not been detailed in other Lux builds. I'll leave the other vagaries of her character to other guides. Learn her combo, and you'll dominate with Lux.