Not Updated For Current Season
Sorry for my english.I hope you will understand.
First i buy Doran's Ring and health potion.In late game you can sell ring and buy Zhonya's Ring.
Than you should buy Archangel's Staff for mana regen and ability power.
Catalyst the protector for mana and health and later you will make a rod of ages from it.
You also need a Rylai's Crystal Scepter for AP and health ,because Lux do not have a lot of hp and she can be killed by a few stronger atacks.
Abyssal specter and Sorcerer's Shoes are good to maximalize your spell damage.
Ghost is good when you want to escape a fight or you want to kill somebody who is runing away.
And cleanse is also good for your survival.