Here i will explain my build to you.
I allways start with dorans ring because its good, you get hp ap and mana renegation.
The second item should be boots, but don't buy full boots before you are finished with your Rod of ages. After rod of ages rush to Rabandons Deathcap for dmg.
After Deathcap buy Rylai's crystal scepter. The reason you buy Rylai's is the slow you get when you cast a spell. The next item is the most important item in late game, it's the migthy Lich bane, Lich bane makes your attacks make the same amount of dmg as your spells the cooldown is 2 sec. Then you sell your dorans if you not already have and buy Void staff. Void staff gives you 40% magic penetration and help you deal a lot more dmg in late game.
There are some other items thats good for Lux depending on the game. They are Kage's lucky pick but if you buy this item buy it in the beginning. If you have a lot of ap carries in the team buy Will of the Ancients if you are many who buy this item in the team you get extremly much spell vamp.
Why you should not buy (1) Archangel's staff, (2) Ionian Boots of Lucidity, (3)Mejai's Soulstealer.

1: The reasons not to buy Archangel's staff are: 1 If you have this build you already got very nice mana renegation, 2 It takes a lot time to stack the mana you get from Tear of Goddess, 3 You will get a litte more ap from this in the end but then it doesn't really matter you got a lot better
items to buy than this.

2: The main reason not to buy Ionian boots of Lucidity are: You won't have a lot shorter cooldowns and it doesn't really if you get one second shorter cooldowns it wont help you as much as Sorcerer's Shoes.

3: If you play a ranked game or a normal game and you are level 30 you won't be able to stack it (you will end up with 3-5 stacks or something).

This build is for mid game. But never go against a Le Blanc in mid because you will feed him if he got any skill at all. You should constanly try to last hit minions. The reason you start with
Lusent Singularity, you can push and harras your opponent in early game without taking any dmg yourself. When you got your ult you should gank a lot your ult has a pritty nice range and a short cooldown.
When you nuke you opponent start with Lusent Singularity in about the same sec you cast Light Binding when you hit him cast you ult and ignite. In all levels before lvl 12 none should survive this if its not Rammus or some noob only bought magic resist. In the team battle stay in the back and constatly cast all of your spells. Try to hit the entire team with you ult for maximum dmg.

My recommended spells for Lux are as you see in the build Ignite and Flash.
The reason i have ignite are its great against a lot of champs its great to finish of champs. Flash you need to have if you play Lux its great to get out of battles with and escape enimies.
There is a couple of other spells that are good with lux. They are Ghost, Teleport (if you are a new player on lol), Clarity if you dont have good mana renegation in your runes and masteries,
the last spell that are possible for Lux are Surge and if you play support Lux ClairVoyance.

My recommended runes for lux are runes Greater Glyph of Clarity x9, Greater Seal of Clarity x9,
Greater Mark of Insight x9, Greater of Potency x3. The reason i have theese runes are because they fit perfectly with my build. I got ap Quintessence for more dmg in the beginning (it doesn't make that much of a change in late game).The mana renegation runes are good to have in the entire game because they make you be able to constantly cast spells and harras your opponents without takeing a lot of dmg yourself. Magic penetration runes are good for more dmg.

Your spells are good for helping your teamates, to gank, for cotrolling the lane, to do dmg from distance.
Spell Q Light binding: A good spell for ganking and it makes a great combo with your ult and your E spell.
Spell W Prismatic barrier is a shield who protect you and all your teamates who gets the sheid from all incoming dmg lux gets the shield when she cast it and when it comes back. A great spell in teamfights it can somtimes save your teamates.
Spell E Lucent Singularity: its a great in lane its alson good to detect ganks. Where ever you cast the spell you get vision of that area. It also slows the enimies who walks in it.
Spell R your ult Finales Funkeln: It's a long range skillshot that deals dmg to all enemies it hits. It's range is long it makes a good combo with you Q spell. you can use it to finish of enemies. It's cooldown are short so use it as often as you can. In teamfights try to hit as many enemies you can to do

The Masteries i recommend are common spellcaster Masteries 9-0-21. The reason for the offencive spellcaster memories are the magic penetration you get from the 9th point. It's pretty important you have that point.
21 in Utility are good you get cooldown reduction, mana renegation, increased xp from minions and monsters, movement speed, a little bit spell vamp.