1) I prefer starting with a doran`s ring giving mana regen and hp wich are essential in early game.
2)Lux needs a lot of mana so i continue with saphire crystal.
3)After saphire crystal i would go for boots for extra speed and its easyer to move from 1 place to another for ganks and so on.
4)I take catalyst and after that rod of ages ,wich is very important for lux giving her the survivability she needs to resist more ,and so she won`t be 1 shot kill.
5)I upgrade the boots to ionia ,because of the 15 percent cdr .
6)Depending on the fight situation buy mejai soulstealer . If your team owns the opponent in early game you can take mejai before rod of ages.
7)Archangel staff,as i said lux needs a lot of mana and this item is the best for her.
8)Rabadon ,an item that you need on every ap heroe.

9) In case your team isn`t making any kills or you die too much loosing mejai stacks,just sell it and buy rylay scepter.

I love the 9/0/21 build
From offence you need to take Archaic knowledge for the magic penetration.

Support now.
Wondering why i spent 3 points in good hands? Well i bielieve that in late game 1 death counts a lot ,and the less time you spend dead the more chances your team will have to win the game... or not die because 5v4
Expanded mind.. every1 needs mana
Greed ,you wont say no to more gold
Meditation helps you ergain mana in no time so it wont be needed to get back at base every time you remain without

I take light binding first.You can stun an escaping enemy and also you can escape a gank using this one.
After that i take lucent singularity ,being a very good spell for harrasing enemy champions,and it`s also good for farming ,but it consumes mana very fast
I suggest taking the prismatic barrier at lvl 7 depending on how your allyes need it.
The ultimate .Pretty long range , very good at killing enemyes that stay near tower with low hp.

3 hp quints .Having more hp in early game gives you a huge boost.
9 marks for magic penetration .More dmg will only help you
9 seals for mana regen. Mana is very important for lux
9 glyph for cdr ,important for lux