While there are certain champs that have more reliable burst, or put out more raw DPS, a Lux that knows how to shoot will be a game-changing force in team fights. This is ESPECIALLY true in mid-game, when Lux's ult hurts the most (note that Lux's ult cooldown drops significantly at level 16, but it doesn't melt faces like it does when everyone is lower than level 16)

When a Lux gets fed in early game (even just 3-0 or something like that), she will become extremely scary. Jungles will be scared to gank her without obvious gap-closers (like Nocturne/yi's ultimate). Ranged and melee carries will wet their pants at the thought of being snared by her Q (anyone caught in a Lux snare is a "please kill me" signal), and even tanks will generally not have the magic resistance to approach her confidently.

Basically, Lux is THE mid-game menace if played right and retains extreme utility late-game if you follow this guide.

Note: The guide is all-text right now (11/11/2012) and I will update when I figure out how to add the picture in. If you're not familiar with the names of Lux's abilities, this might not be very useful right now.

In terms of masteries and summoner spells, I will just describe the differences between this guide and some others.

The norm for masteries is 21-0-9, and I have that too. Due to this Lux having teleport, I don't use summoner's wrath, and I try to max her AP with mental force. I ignore attack damage, assuming that players can time last hits well enough during the laning phase, looking to maximize AP in order to make Lux as potent a ganker as possible once she hits level 6.

For runes, go with conventional wisdom. Greater mark of insight all the way (magic pen.), greater seal of vitality (health points), greater glyph of force (ap), greater quintessence of potency (ap)

Flash is chosen for a million different reasons. You can initiate at a huge range with flash (flash + q or e goes a LONG away) or you can escape a gank with it. It's a MUST.

Teleport is chosen over the more popular ignite as described in the next section.

As a mid-game telegank stomper, you need very good map awareness. Look for situations in bottom and top lane where you can teleport and melt the enemy team's champs. This becomes especially possible at level 6 due to your ult. If you see an enemy at 3/4 or less health, and you can land your q, you can almost always kill them unless they are either heavy in magic resistance or if they dodge your ultimate (vlad is one champion who can do this very easily).

Also make sure you don't teleport yourself into a bad situation that will get you killed (unless you KNOW that you can secure 2 kills by sacrificing your own life)

Why teleport over ignite? Two major reasons. First, I feel that lux shouldn't ever be in a blow-for-blow situation where ignite is necessary - not should she be that close to the enemy. There are exceptions, like when fighting a melee enemy champion, but

Always start off with boots. Lux needs boots to dodge, and to harass with her E (Lucent Singularity). You have to predict where champions will run when you use your E, because after getting blasted with it 2-3 times they will start getting annoyed.

Build the boots into ionian boots of lucidity, or sorceror's shoes depending on how your jungle and you are doing.

If you are dominating or you're fed, I think sorceror's shoes are the natural pick to add extra magic penetration to burst down your enemies to zero hp. If your jungle is doing exceptionally well, you may want to go with the extra cooldown so you have more chances to snare the enemy mid when your jungle is nearby and ready to gank.

After that, I recommend rushing either rushing a deathcap or going for Athene's unholy grail. This depends on the enemy composition, and how you're doing. If you're doing poorly, the unholy grail will allow you to stay longer in mid and farm up a bit. If you're ready to start teleganking, the deathcap will give you unbelievable damage in mid-game that will wreck enemies in teamfights. After you go have both your deathcap and your unholy grail, the game starts to get more teamfight oriented, and Lux's q gets more important than ever.

Morello's evil tome is a decent pick, since it gives a very nice extra 20% cooldown reduction (you can start spamming your ult very frequently at level 16 with cooldown boots, athene's unholy grail AND the tome)

If the enemy has a lot of CC, you'd be better off with a Rod of Ages first. It gives a huge amount of health, and extra mana to help you spam your skillshots. This makes lux less likely to run out of mana.

The last two items should be built based on the enemy. If they have an amumu, for instance, you might want to consider a banshee's veil so that his ultimate doesn't completely shut you down during teamfights (their ad carry will finish you off in a few shots since your only defense is your shield and flash.)

An obvious choice for a magic-resistance stacking enemy is a void staff, which will let your spells actually do something to the most well-geared tank.

If you find that you're able to get a few autoattacks in during teamfights, a lich bane is the obvious choice (they will not realize just how much your autoattacks hurt until it's too late)

The last viable option is the abyssal scepter, which an all-around great item if nobody else has one. If your team is ap-heavy, either have someone else get this by mid-game or get it yourself - it reduces everyone's magic resistance by 20! That's a big difference.

Archangel's staff is only viable if you have a fully-stacked tear, which means that you'd have to commit to it earlier. While Lux is mana hungry and would benefit a lot from archangel's, other items bring a lot more to her utility in mid-game (when she is at her peak)

Overall, everything is situational but I emphasize cooldown reduction a lot because of the late-game dynamic.