Turns out that Lux is not only an excellent CC but her damage output can be decimating to the entire enemy team right from the start of the game leading to her carrying the team in team battles. The key thing to Lux is that all of her abilities are long range, giving her the ability to harass, CC, gank, and deal damage as well as get the kills of any runners all without getting into the center of the fight. The downside to her having very long range on her abilities is that Lux is has long cooldowns on QWE and is completely skillshot based. Miss a shot and you'll have to face the consequences. The upside is that's what makes Lux more difficult to play and much more fun to win with :)

Build Pros:
- Long Range damage output
- Survivability with CC
- Lots of mana regen
- Some HP gained from items
- Added Deathfire Grasp clicky ability

Build Cons:
- Still squishy even though Rod gives some HP, so don't let them get too close!
- Cooldowns on QWE abilities are kind of long. If you can, space out the use of Q and E so you always have CC handy.

I find this is a pretty solid item build. By the end of the game if you have full stacks of Soulstealer as well as all of these items and are buying elixirs you'll have around 850AP to fool around with as well as a Deathfire Grasp clicky allowing you to deal out massive damage.
Meki Pendant: Lux needs mana regen right off the bat. Helps save $$ because it's used as a component for Archangels.
Kage's: Cheap AP boost, pays for itself, later used to make Deathfire Grasp.
Soulstealer: Key item right here. Building it up to 20 and keeping it there is a definite goal. If you can do that the rest of the game is cake.
Sorcerer's Shoes: Some people choose the cooldown boots, but Sorcerer's shoes makes all your abilities more powerful which definitely helps when using the lazer as a last-hitter for runners and you can make up for the loss in cooldown as well as paying for your low level items later by slowly building a Deathfire Grasp starting with Kage's.
Archangel's Staff: Gives you the mana regen you need as well as ability power.
Rod of Ages: AP, Health, and mana (which Archangel's will use to boost your AP more). Makes Lux able to take a hit or 2 without really sacrificing AP to get it.
Deathfire Grasp: You waited to build it so you could get some added $$ from Kages. Now you have it and you have reduced cooldowns, AP, all the mana regen you need to stay in the field, and oh yeah.. a new ability that gives you a targetable ability (not a skillshot?) that deals a hefty amount of damage.
Rabadon's Deathcap: Chances are you've won already. But if you didn't, now you will. At this point you should have all the AP in the world. The enemy team will run from you cowering at your ability to stay far away with CC and deal enough damage to kill everyone.

** Q Ability (Snare) ** Won't say much on this. Obvious use is CC. Save it primarily for that. Can also be used for damage (make sure to get your passive burst off by combining it with an attack). It's a skillshot that doesn't go through minions so be careful. Excellent snare though (snaring 2 champs = $$). Use it wisely to keep your distance and stop champs from chasing you as well as stop them from running away. Also use it in conjunction with your lazer to make sure champs are locked in place and already hit with your passive when you're firing. Great for kiting as well (time this and E wisely).
** E Ability (Lucent Singularity) ** This is our primary ability. Lux's E ability is long range, AE, and can be used through creeps. $$. Great skill to level for damage both to champs and creeps. Also grants vision (not see invis) allowing you to peek over walls, check bushes, and aim your other abilities. Also great for slowing enemies (CC). Use it to deal damage in an area (to creeps and champions) and harass. Also use it when ganking, and to help keep from being surprised by an onslaught from the bushes. Remember in order for Lux to stay alive she has to be far away from the center of the action. Slow enemies at key moments to run from them or keep them from running away and only blast the singularity when they have reached the edge and are about to leave the slow field. Also great for kiting (time this and Q wisely).
** Passive & Ability Spacing ** If you can, try to space out the use of Lux's Q and E abilities. By doing this you effectively reduce the time where you're sitting on cooldown without the ability to CC. Also by doing this it gives you the time you need to attack after using your Q/E abilities, thus activating your passive (much needed to deal proper damage with Lux). Doing this properly makes you an effective kiter. By the time they figure out you're winning it's too late (lazer'd).
** W Ability (Shield) ** We don't really level Lux's W ability (shield) until late game, but it's still useful to put 1 point into. Remember to shoot it off at the right time to shield teammates and yourself, but focus more on using your Q and E abilities wisely.
** Ult - Lazer ** Accurate use of the lazer is key. It's much easier to aim at an opponent who is running directly away from you. It's usually fast enough that you can just aim right on them, but try to guess the path they will run and fire. Also the lazer allows Lux to engage in a fight from far away. So if you see some allies needing help, ghost over and shoot your lazer immediately if your teammates really need the help. Otherwise wait it out to use the Lazer in conjunction with Q or E to deal more damage via your passive. Remember that the lazer sets off your passive as well as re-applying it! If a fight is going well wait to use the lazer until there are runners / champs with low health and finish them off easily with proper aim.

Lux works great mid, but can also be excellent teamed up with the right hero in a lane due to her ability to harass and CC. Obviously if you're looking to carry then going solo in mid is best.

Right from the start get Lux's E ability and start harassing with any full mana you have. With mana regen from her meki pendant as well as your runes/masteries keeping mana up shouldn't be a problem as long as you don't miss your shots. At level 3 you will have 2 points in her E ability, you can really start dishing out damage then. ** Whenever you hit an enemy with the E (or any) ability make sure to do a standard attack setting off your passive. That's really the key to dealing damage with Lux.

Never forget while harassing to always grab minion kills (JUST the last hit, don't autoattack the minions) Lux's E ability is also useful for this while harassing by giving you the ability to deal a high damage last hit to anything affected by the blast. Just time everything properly and you can last hit the minions easily (especially in mid).

Try not to go back to town ever. Force the enemy to go back to town instead. If you do have to go back to town I suggest waiting till you can buy something useful (at least boots & Kage's) and using the Ghost summoner ability to get back quickly.

You should have leveled up your E ability sufficiently to be dealing some decent damage. At this point you will have Kage's which will hopefully pay for itself soon enough, as well as a Soulstealer and Sorcerer's Shoes and be well on your way to building Archgangel's. Now's the time to keep an eye out on the minimap for everything going on around (especially if you're mid). If you see some low health enemy heroes in lanes don't hesitate to burn up a Ghost and run over to them. Surprise them with your long range abilities and take them out as they run with your ultimate. Don't sacrifice yourself for kills, just get them when you see the opportunity to take them and run. Remember you're not just getting kills for yourself, you're getting kills and assists for your Soulstealer.

Building up your Soulstealer's stacks is of highest importance. Ghost and flash are useful to keep yourself faster than the enemies and far away from the center of the fight. Don't die, preserve the stacks!

Also of note is that you should be able to solo Blue/Red buffs at this point as well as easily taking out the 4 little wraith jungle guys with E and some attacks. If they're open/nearby then go for it. Leveling faster than the enemy is important too, and E's ability to deal damage will help you a LOT with that now.

By now you should be finishing up your items and have plenty of Soulstealer stacks. If this is the case, your abilities should be an enormous help in team fights both for CC and for damage (oh and lets not forget shielding). Cooldown of your ultimate with full stacks of Soulstealer + Deathfire Grasp should be around 25 seconds! This lets you use the lazer at the beginning of fights as well as at the end on fleeing heroes. With all your abilities and Deathfire Grasp you can dish out some mean damage whether you're hanging out around teammates or pushing lanes with your E ability. Still be careful to stay far away from enemies and preserve/increase your Soulstealer stacks by staying alive. You can take out stray enemies as you see fit. You might not be able to kill everyone in a 1 on 1 fight, but you can test the waters out just by staying far enough away from your opponent by using CC wisely. By the time the enemy is fed up by your CC and chasing you, your teammates probably caught on and are helping you take him out anyway.

Lux is a beast. You can get up to 850ish AP by the very end of the game and still have some added HP, lots of mana regen, and a Deathfire Grasp clicky to fool around with. The enemy team will fear getting close to you, which is exactly what you want.

You do the math: