Pros:

*Long Range Nuke power
*Can Save Or Break Anyone with her Snare and Slow
*Very Very Useful In Team fights
*Short as hell ult that makes people cry

Cons:

*VERY SQUISHY
*If you miss your snare when getting chased, Good Fight.
*Easy target for assassins

Lich Bane why? Well if you utilize your passive well this item is perfect, that bonus damage from your A.P plus that extra damage from your passive makes you even more deadly.

No rod of ages? Playing lux you want that A.P asap!! rod takes time to get to full potential

Why boots so late, when playing lux you play passively, dont be in the front line in team fights, you wont need boots to escape if you stay back. Also when you get boots later you can get an a.p item faster. NEED A.P ASAP!

Passive: Illumination - Lux's damaging spells charge the target with energy for 6 seconds. Lux's next attack ignites the energy, dealing bonus magic damage (depending on Lux's level) to the target.

Fairly simple damage someone with a skill and follow it up with a nice basic attack, this works very well with lich bane

Q: Light Binding - Lux releases a sphere of light that binds and deals damage to up to two enemy units, dealing 50% effect to the 2nd unit struck.
Fires a ball of light towards a target location, binding and damaging up to 2 enemy units. The first target takes 60/110/160/210/260 (+0.7) magic damage and is bound for 2 seconds. The second target receives 50% of the effect.
Cost
60/75/90/105/120 Mana
Range: 10000

Great Snare especially for ganks, remember that you might need to bounce it through a minion to hit someone. Also this can save your life, snare and run; if you miss well GL.

W: Prismatic Barrier - Lux throws her wand and bends the light around any friendly target it touches, protecting them from enemy damage.
Lux throws her wand to the target location and back, protecting herself and all allied champions it touches from 60/85/110/135/160 (+0.35) damage for seconds.

Daaaamn this skill is so usefull, can save your life and a teammates life. Aiming this skill is key, aim it infront of where your ally is moving too and position yourself after it is cast to ensure it reaches its target. When escaping, use this skill ahead where you are running too as it lessens the time of when the sheild comes back at you.

E: Lucent Singularity - Fires an anomaly of twisted light to an area, which slows nearby enemies. Lux can detonate it to damage enemies in the area of effect.
Creates a zone that slows enemy units by 20/24/28/32/36% (zone lasts 5 seconds). Can be detonated to damage enemies in the area for 60/105/150/195/240 (+0.6) magic damage.
Cost
70/85/100/115/130 Mana
Range
1100

The big nuke of lux, one of her main sources of damage, Max first!; when aiming this skill in lane i tend to aim the skill behind them but still in range of them as the natural reaction of someone is to move back, here is a picture to better show what i meanSee how my lucent is placed on and behind her.

Using her ult properly is key to getting them smeeexy kills so I am dedicating a whole section for it.

KEY THING!!!

When your are aiming your ult the range on it isn't exactly what the skill shot aim tells you, here is the range her ult actually has