I usually put a point in q and then e and then w and max my q first then my e and then my w but it really depends on how the game is going and who my match up is.
If your skill shots aren't that good, start with your e.
when using your q as support, try to hide in bushes to get the element of surprise and lessen their chances of being able to dodge it because Lux is vulnerable and at her weakest when she doesn't have her q. Missing it and staying too close will usually leave more susceptible to being punished.
As always, put a point in your ultimate whenever possible.
Try to land a snare before using your ultimate or wait until the enemy you're targeting has been cc'd by another ally.
Lux ultimate is powerful and does a lot of damage. You can use it to steal dragon (know how much damage it does and watch the drags health (beware of enemy smite).
If an enemy is running away, position yourself diagonally and aim slightly in front of them so that they either have to:
-stop and wait to avoid running into it
-flash over it or heal
-use their ultimate to dodge yours (eg; Zed, Ahri)
-run through it and take the damage (potentially killing them or making them much easier to kill for an ally with another global ult (jinx, ashe, ezreal, draven) or an ally with a gap close who may not have been able to turret dive them because they had too high of health before you ulted. Allies with a gap close may include: jax, dianna, akali, ahri, irelia, etc.
-pop their zhonyas and have to sit in it long enough for your team to catch up to them
-possibly proc their guardians if you hit them and deal enough damage to kill them. Then you know it'll be down for another few minutes.

I find it fun to use runes that maximize Lux's burst potential and give her a little bit of mana regeneration to compensate for her high mana costs early game.

- 9 greater marks of ability power
- 9 greater seals of ability power
- 3 greater quintessence of ability power
- 9 greater glyphs of mana regeneration

Ferocity:
5 points into sorcery
1 point into feast
5 points into natural talent
1 point into oppressor
5 points into piercing thoughts
1 point into deathfire touch

Cunning:
No points in this column.

Resolve:
5 points into unyielding
1 point into explorer
5 points into runic armor
1 point into insight

For mid lane I start with dorans ring for the ap and the sustain and two health pots. On my first or second back i sell my dorans ring and build abyssal scepter, rabadons death cap, zhonyas hourglass, ludens echo, lich bane and ionian boots of lucidity (I build lucidity for the cdr to provide more constant damage, if they have mr I would recomend opting out for sorcerers shoes). (Build in the order that will benefit you most at the time)

My support build starts with the first part of frost queens claim and 3 health pots and generally proceeds to finish building into frost queens claim, zhonyas hourglass, rabadons death cap, rylais crystal scepter, ludens echo and ionian boots of lucidity.
(Build in the order that will benefit you most at the time)

Ignite
I would never recommend taking ignite. If you're in range to use it, you're too close. If you want to be really aggressive early game it can be useful but late game it's usually not very beneficial in comparison to other summoner spells.

Teleport
If you know how to balance roaming while keeping up with cs (mid), protecting your adc (sup), defending your lane and attaining objectives, teleport is a nice summoner to have. It gets you back to lane quickly and can give you an xp advantage in some cases. Teleport also helps give you more map presence to make roaming much easier and quicker (and let's be honest, having a lux gank your lane even just to throw a snare is always appreciated). Lux is an aggressive, bursty champion and being all over the map will help you get fed or help you to get the rest of your team fed.

Barrier
Using barrier and her shield together is good for absorbing a lot of burst damage from champs like zed.

Exhaust
Lux has a nice chunk of cc (q snares and e slows). As support and sometimes mid I like taking exhaust as either cc, or to provide an escape.

Heal
I usually only take heal when I'm going support and my adc isn't bringing it so that i can use it together with my shield to save them and/or myself in case of an emergency.

Flash
Lux has no escape really other than throwing her q and running. I recommend always taking flash with her to compensate for her lack of mobility.

Pro's:

Lux has a pretty long range and does well against most mele champions.
Lux provides a lot of burst damage
Lux has a comfortable amount of cc
The Lux e grants vision (also inside of an akali shroud)

Con's:

Lux is very squishy
Lux has very limited mobility and is easy to pick off if you get too close
Lux's damage tends falls off late game if they build a lot of mr (build void staff in this case)

Lux is good for peeling. Her q snares and her e slows. Both her e and q are powerful in team fights because her q works if used right to allow your team to group and easily pick off one or two enemy champs. Your e is a pretty big aoe range and if your hit several enemies and pop the passive on them, you will be dealing a nice chunk in damage. Her e also grants vision when thrown somewhere on the map covered by fog of war
(( like hmmm are they taking dragon? Throw e over the wall to find out and maybe even steal it by popping the e or ulting in while you have vision )).
Lux's w (shield) is great because you can use it to protect not only yourself, but your entire team.

Lux has fairly high mana costs, I would not recommend using her abilities to farm early in the game. She needs items to stay strong late game so make sure you keep up with your cs mid lane (or top, I've tried it and it is fun).
If you are taking Lux support, you should not be taking cs and it is usually best to take a gold inc item like frost queens on lux as it gives added cc, 2 gold per ten seconds and when you hit an enemy champion with an ability you will receive tribute gold which is nice on Lux because she is a pretty aggressive support champ.