Lux is a very powerful caster.She is a great champ for team battles,when you reach lvl 16 the cooldown of your ULTIMATE witll be

24 secs

Your spells are really helpful when ganging someone.Once you stun the enemy he is all yours.

When you play Lux you would wanna play on MID. By spamming your Lucent Singularity you will keep your opponents health low.All you need to do is wait till lvl 6 ,then you attack him with everything you've got when he starts running you simply use your ULTIMATE and there you have a kill :D.It is very IMPORTANT to keep your enemy's health low or you might not kill him at lvl 6.
After that things are getting easy.You start going around lanes and getting some more kills.

For summoner spells I go with Clarity and Heal that way I don't need to go back for health and mana,and I can stay on the battlefield for longer time at late game.Some other good spell to use is

ClayrVoyance

It is very helpful when an enemy is running on low health and you cant see him so you can aim your ultimate.

These are my tips for playing Lux hope I helped you guys pls rate and comment this is my 1st build ever ;)