Most Lux’s make the mistake of grabbing Light Binding first. “Ooo, I need some CC in case something happens before laning starts!” No. Light Binding is not what you want for prelaning. Light binding is a skillshot. Lucent singularity will do the same damage at lvl 1 while being MUCH more forgiving or your aim, and providing CC with slow. It can be used to check bushes, and can hit a whole team in a fight over Blue, rather than the mere 1.5 enemies that Light bindings would. Also, you want lucent singularity in lane to push / farm as soon as possible, and a lux without it appears exceedingly pathetic. Take Light Bindings second. For all my harsh words, the snare is handy. Take another lvl in Lucent Singularity at lvl 3, the extra lvl is essential to laning. Then take a lvl in shield. It will save your life at some point. After that, Max Lucent Singularity, followed by Light Bindings, and lastly shield, taking The Lazer at 6, 11, 16.

This build was designed with CDR in mind. With the given runes and masteries, a CDR within .11 of 40% can be achieved after farming only 1885 gold and buying Ionian Boots of Lucidity, followed by Fiendish Codex.
While the items do not favor mana supply, the summoner spells and runes address this issue. Clarity and flat mana regen seals are sufficient to support a Lux with only meki pendant or fiendish codex for mana regen at low levels. At higher levels, the mana regen per level quints kick in and generally eradicate any mana problems. And if there are, you still have clarity. If you find that you still need a little extra mana support, and the quints haven't kicked in yet, I suggest buying the sapphire crystal that will later be turned into sheen after finishing the IBL and FC.
Remember, have 2 health pots any time you can afford them, and pop one as soon as you lack enough health to use all of it. Pop the other if some douche DOT’s or Ignites you.
If the game isn't going disastrously, I suggest rushing Majai's after IBL and FC, as a properly played Lux can (and should) go a whole game without a single death (even while losing) or at least no more than 1-2. Even with only assists, if you are not dying, your Majai's will stack quickly. If you are having a bad game, skip the Majai's and head straight for Rabadon's, adding Rylai's to the end of the build, before or after turning FC into Morello's.
Lichbane is a wonderful item on Lux. I suggest getting it as soon as Rabadon's is finished, as the Lichbane damage stacked on Lux's passive can bring a well placed autoattack to the strength of one of her spells, adding a significant attack to her arsenal. However, if the other team is building magic resist, I would suggest putting together a Void staff first.
The Morello's will not add any CDR, as it is already above 39% with FC complete. However, when all other items are done, there is nothing left to do but build FC into something. Morello's will give more AP than Deathfire Grasp, but if one prefers Deathfire for the effect and can remember to use it, then by all means, build Deathfire. If you are thinking Nashor's Tooth, then go step on a Teemo mushroom.

Clarity is essential as specified above. Also it allows you to be a good little support and help your team mates by giving them mana when they need it most.
Now, you might be saying “Why would you not take Flash instead of ghost?! You are squandering your above-level-12-priveliges.” Now, you can take Flash if you really want to, but I recommend ghost, because with Lux’s abilities it is just as good an escape mechanism, but it also allows for correction. If you suddenly need to flee, but after 3 seconds find that you need to turn back, the Ghost you just popped will speed you towards your objective. Your Flash will grumble that you should have figured it out earlier and now it was too late cause you jumped the whole distance already and no refunds.

Masteries are standard mage 9 / 0 /21, making sure to nab all the CDR possible (9%)
For Marks, magic pen of course. Glyphs of CDR allow IBL and FC, in tandem with masteries, to put the CDR at 39.89%, nearly capped, for mearly 1885 farmed gold. Seals of mana regen are useful early game. Quints of mana regen per lvl, as stated above, are a powerful source of mana later in the game, and are very effective in removing mana problems. They are also very helpful with other champions. A champion designed to function with low mana and mana regen can spray their abilities with impunity late game without even having a mana or mana regen item if they have the 3 Quints of mana regen per lvl.

You may say, “What’s with this obsession with CDR? Your build is based around getting it as fast as possible! Shouldn’t you be rushing AP as hard as possible?” To that I say, Lux is incredibly limited by her cool downs, especially early game, before her spells are very strong. Being able to cast them at nearly twice the speed (40% CDR) will double her effectiveness. It brings me great sorrow to see a Lux not build CDR, for she is putting all that AP to waste. You have 500+ AP? So do I, but I fire it 25% more often than you, so, effectively, I have more than you.
And there is something to be said for having a laser on a ~25 sec cooldown. Something wonderful, in fact. It happens to cool down at about the same speed that minion waves are produced. Which means that a Lux with 40% CDR is one of the most effective anti-siege weapons in the game, capable of removing any approaching enemy minion wave long before the get anywhere close to the inhibitor tower (or before you can even see them, for that matter). Lazer farming is a hilariously effective way of getting gold quickly without endangering one’s self. Press R to push lane.
Also, having the lazer on 25 sec is vital for team fights. Do you want to blast their team once? Or do you want to blast them once at the start and once near the end?
Basically, do you want a 40 sec lazer or a 25 sec lazer?
“BUT I WANT TO RUSH AP!!” You’ll get your damn AP, the build provides you with 600. You’re building a rabadon’s and a majai’s for Christ’s sake.
You may say “Hah! I don’t have to use your build! I’m going to get Blue and have 40% CDR and not have those mana problems at all.” Really? And who's going to give you, a lowly Lux, Blue? You’re not worthy of it in their (misguided) eyes. Your powerful, hard hitting AP carry needs that Blue, cause they are SOOOO OP with it. And what if you have a jungler? Please.
And if you by some chance happen to convince them to let you have blue, what happens when your team starts losing? Are you, frail, squishy Lux, going to go into unguarded enemy territory to get blue? Don’t make me laugh. If you want to rely on the luxuries of Blue, you need to provide them yourself, and you will do all the better because of it, because you will have them at all times and under all circumstances.
Another complaint may be “I want Doran’s ring first, it’s a great starting item! Can I take it instead of Meki pendant?” No. It’s a terrible starting item. It’s got less mana regen than Meki pendant, you don’t need that measly bit of AP, and 2 health pots are much more forgiving than an extra 100 health. Also, it would make IBL an FC take longer.
Now you may also note “Your build has a significant lack of defense. Why aren’t you building any survivability on Lux?” Go sit in a corner and think about what you just said.
You’re back? And you still don’t know what was wrong with that statement?
Fine, I’ll explain. (imbecile)
Lux will never not be squishy. Don’t waste items trying to make her tough. It’s not going to work. “But how do I not die with her?” you might be whining. Stop whining. Your best and only way of staying alive with Lux is escape-artistry. You have wonderful CC from your Light Binding and Lucent Singularity, and a well-used shield in tandem with a health pot will counter untimely damage or DOT’s that might be thrown your way. Ghost plus good use of skills makes Lux surprisingly slippery. Get good at dodging skill shots and landing your own, it’s the only way to survive consistently.
And you will enjoy having built raw AP on 40% CDR when you do close to 1000 damage with your lazer and nearly as much with the follow up auto attack. Every. 25. Seconds.