last hitting is the most important skill in the game LoL. Last hitting means to last hit/ killing blow on a minion. you let your minions do all the damage on your enemys minions and you last hit for the gold. the more last hits u get, the faster you get items.
You would want to last hit because it prevents a big chance of a jungle gank. A gank is a ambush from the fog of war.

video about last hitting: http://www.youtube.com/watch?v=0OO7epPhXXI

pros
good damage outplay if you land your combo
low cooldown on her ult
good range on her ult
double rainbow

Cons
very squishy
hard to master
mana hungry at early lvls

i take flash and ignite because flash can get me out of sticky situations and ignite can give the little boost of damage needed to get the killing blow.

you want to use lux's passive as often as possible. the combo that i use is throw my e and land my q. make sure you are positive to land your snare. when you land your snare auto atk and activiate e again and atk. if they are low health after that combo use your ult to finish them off and maybe ignite just to secure the kill.

http://www.youtube.com/watch?v=ixB3l0zOeUE
Watch it at 3:16