This is my build on Lux whenever I play. And I'll explain everything as to why I pick these certain things and I'll include tactics on how to become that pro Lux you've always wanted to be.

The runes are kind of self explanatory. I have scaling runes to help Lux be most effective when she outlevels her opposing enemies.

I had magic penetration runes to shut down tanky anti ap champions. IE Volibear.

I got mana regeneration because especially early game does Lux run into mana problems if you aren't smart with your mana.

The masteries are set AP based and I put the Runic Affinity in because Lux if played aggressively is kind of reliant on ancient golem buff (blue).

Early game she becomes heavily reliant on any mana if you need to play aggressively. This often happens when you need to shut down the lane with heavy damage and zoning the target back to the nexus at far distance. An example would be LeBlanc. She does heavy ap damage when she gets close so putting her behind her minions is the best way to shut her down. If you're matched up against an burst damage mid you might want to get mana potions instead of h pots.

As was said before, the h pots can be traded in for mana pots if needed. Also, you're probably looking at my build saying, "Why not Lych Bane first?". The reason I don't rush Lych Bane is because I don't play aggressively with Lux at first. Considering she is easily targeted, I stay at a far distance when I play her. Shooting my abilities to harrass until I know with confidence that I can go in for the kill.
The first item I focus on is |Boots of Lucidity|. The reason I focus this first is because by level 3 you're going to have their jungler in your lane, especially if you play her passively aggressive. This gives you the edge to a faster cc in lane. Also, later on this helps you make that game winning ultimates in team-fights more often.
The second item I focus is |Sheen|. The reason I focus this is because not only does it give you mana and ability power but it makes your normal attacks hurt alot more, this allows for a much smoother cs cleaning.
The third item I focus is |Rabidon's Deathcap|. The reason I focus this is because it gives you the highest ap boost you will find in the shop. By the time you're buying this you're ultimate should already be doing 300-500 magic damage, boosting it up a significant amount.
The fourth item I focus is |Void Staff|. This is optional. I only pick this if they're countering AP very hard. 40% magic pen + the added AP = one hell of a kick in the face.
The fifth item I focus is |Lich Bane|. The reason I focus this is to add that extra damage to my after ability attacks. Allowing me to combo more effectively to bring my opponent to their knees.
The sixth item I focus is a |Will of the Ancients|. The reason I focus this is because even if my team isn't focusing AP this has the best spell vamp and can give you the spotlight in a teambattle. When/if you buy this, you're more likely to get focused down hard. Make sure that you e into bushes you don't trust so you don't get ganked and remember if you're up close behind enemy lines to never waste a q or a flash.
The last item I focus is a |Ryali Crystal Septer|. The reason I focus this is because late-game you become focused. Let's face it, Lux may have an insane amount of cc but she isn't unstoppable. She can be easily countered by an Assassin or a champion that uses an ability to get closer to you. Having the extra health and using abilities to slow your opponent down in a teamfight will give you the extra edge when either escaping or letting your ad team get that change to finish off your opponents.

You're probably thinking, "Why not get your 'e' first?". The reason why I don't get my e first is because it's not very cost effective. It doesn't do alot of damage early game and until it is upgraded 3 times it's almost useless. Almost. However, having that extra security to push the opposing champion back with an early snare will let him know that you're not here to screw around.

1. Max 'e'
2. Max 'q'
3. Max 'r'
4. Max 'w'

Now you're probably thinking a mid carry that doesn't use ignite?? I picked teleport because of two reasons.
[*] One, it gets you back into the lane quick after a trip back to resupply and reheal/remana.

[*] Two, (and this is where it gets fun) the unfortunate thing about Lux's ult is that it doesn't have lane to lane capabilities, meaning, I can't sit in mid lane and ult someone in bot lane. However, if someone decides to overextend too much and is too aggressive I can use teleport to finish someone off. It is especially useful when a player falls behind a turret and you have bot lane warding the place with their support. This gives you the opportunity for a quick easy kill secured.

The following tricks are the ones that I use whenever I play Lux:

Using Lux with teleport you must be more map aware. Have your team ping their lane when someone decides to fall behind a turret and go too low. This will allow you to easily fall back for a few seconds, teleport and finish them off.

Lux's 'w' can be a real life saver. Remember to use it when your opponent uses ignite on you. It can take off up to 5 ticks from an ignite which is more than enough to keep you still alive.

Also, Lux's 'w' can help when you're running away from a person. Remember to throw it in the direction you are going so the shield gets back to you faster.

Always be passive aggressive until you are sure you can go in for the kill.

You never want to be too aggressive with Lux because that will get you killed. Why get in close to your enemies when you don't need to?

Bring down your opponent by harassing him with your 'e' but make sure you are out of range for their abilities.

Remember your 'q' is not a stun. They can use abilities to escape from your 'q'.
Use your 'e' to zone in for your Ultimate.

If there are 4 or more people in the same area it's a good idea to use your ultimate regardless if their low or not. Max level brings your cooldown red of your ult to about 20 seconds.

Getting your 'e' to level 3 + Dorans ring will allow you to 1 hit Caster Minions. Allowing for a smoother farm.

I usually don't go back for things unless they make a huge impact on what I'm doing in lane. So farm until you're level 6, this should give you enough gold to buy tier 2 boots and maybe sheen.

A good match up with Lux is Lee Sin jungling. As he doesn't really require the blue buff to survive in the jungle he can pass it on to the mid carry. This will help you tremendously. Blue buff will help greatly no matter what level you're at.

Pros:

Lux has a semi-instant long-ranged ult that does a decent amount of damage.
Lux has two forms of crowd control.
Lux can farm easily.
Lux's abilities(Except your w) all do extra damage on autoattack afterwards.
Lux can use her 'e' as a sight ward.
Lux's distance allow her to make quick damage without taking any damage in return.

Cons:

Lux is squishy.
Lux is skillshot based.
Lux's ult cannot reach from lane to lane.
Lux is very mana dependent early game and may cause her to run out.
Lux is reliant on blue buff.