Game Phases
Early Game
Start off by buying either a
Doran's Ring, or a
Sapphire Crystal if you're comfortable with kiting without dying.
Early game, you'll find that your spell cooldowns are annoyingly high. You won't get to cast a spell twice while chasing someone down the lane. Not to worry though, you can still get early kills pretty easily. I always lane with a partner when playing Lux. She can probably solo, but it's difficult to get a kill on your own because of your high cooldowns. Start off by weakening the enemy(s) by throwing
Light Binding or
Lucent Singularity at their faces, run in and hit them to use your passive, and then run back. You'll be able to take enemy champions down to half health relatively easily. Then, you can faceroll them with your spells if your laning partner is helping out. Watch out for stuns, however, because when running in to activate your passive, you're also putting yourself into danger.
When you can, go back and buy either a
Mejai's Soulstealer or a
Tear of the Goddess. And then buy the other one. (Though I don't recommend buying a Mejai's until you're comfortable enough to get kills and not die.) Pick up some
Boots of Speed if you have the money to spare, or if you're one of those who desperately needs boots. Because Lux is completely ranged, and you'll have teleport as a summoner spell, boots aren't as important as they are for other characters. The only time you'll really need the speed at this point is for chasing (you have your laser, so screw chasing) and for escaping ganks (if they really have you ganked, there's nothing you can do. Remember, you're as squishy as jello)
Mid Game
Ahh, mid game, where the boys turn to men. Or at least, young men. Or something like that.
Lux is either decent or amazing mid-game, depending on the flow of the game. By now, her spells will be so strong that pushing lanes will be easy (though bashing on towers won't be. She's pretty weak AD-wise). Now you can either keep farming, especially if the game is going slowly, or you can start ganking and moving around. By now, hopefully you've gotten enough mana through your
Tear of the Goddess that you won't be going back every thirty seconds. Lux does burn through mana like a fat kid burns through cakes, however, so you'll still need frequent trips back, unless you picked Clarity as a summoner spell (I did).
Now, get a
Fiendish Codex for the small AP bonus and the CD reduction. You won't feel the reduction that much yet, as your ultimate still needs 60 or 80 seconds to recharge (before the CD reduction), depending on what level it is, and you probably don't have the mana yet to be firing your regular spells in an indiscriminate manner. (NOTE: If you have trouble with the whole living thing, then you can also buy a
Glacial Shroud to later upgrade into a
Frozen Heart instead of a Nashor's (It's actually called Frozen Brain now, but I think you could have figured that out on your own). Also, if you keep dying, then you can consider selling the
Mejai's Soulstealer, but I wouldn't. Instead of selling it, try to hang back and gather assists or runaway kills, because without Mejai's, then you won't really have the power to justify an AP build with CD reduction. Then get a
Blasting Wand for your
Archangel's Staff. By the time you get this, you'll have a large enough pool of mana to both get a nice AP bonus and to fire off your spells like your back in the Wild, Wild, West.
NOTE: If you are pushed into mid game earlier than usual because someone pushed and destroyed a tower early on, you may consider a [item=Soul Shroud] instead of a
Fiendish Codex and
Nashor's Tooth, for the aura, cd redux, and the hp that stops you from dying. It's questionable whether or not you'll be able to get the aura to your entire team, since you're so far away, but it'll help whoever is next to you quite a bit.
If there are any team fights, try to hit as many as you can. Lux can get kills easily because of her high damage output, but she can also get assists easily because she can hit multiple people without much trouble. For now, you should save your ultimate for any runners, because you'll only have once chance to use it per team fight. If you get enough kills, then start working towards a
Nashor's Tooth. I know, the game and some other people recommend Frozen Heart/Brain. You can get that if you're having trouble with the whole "living" thing. If you're playing well, keeping away from the danger, but just close enough to wreak havok, you won't need it as much. Besides, Nashor's Tooth gives AP.
One last thing. Buy some boots now. You'll be moving around, so you'll need the extra help. I prefer
Sorcerer's Shoes for the magic penetration.
Mercury's Treads are useful, but honestly, if you're caught in any CC at all, no matter how short, you'll probably be jumped like flies on poop. You can also get
Boots of Swiftness or
Boots of Mobility, if you're a pro at running in and lasering people they don't expect it, but usually, there are better choices.
Late Game
By now you should have a decent amount of AP. Buy a [item=Zhonya's Ring], and make that a wonderful amount of AP. Also, do yourself a favor, and DON'T FORGET THAT YOU HAVE THIS. By now, if you're murking everybody, they're going to start to focus on you, if they haven't already. Just pop the ring, and hope that help is nearby. If it isn't, at least you got to turn into a gold statue for a few seconds. Not many people get that chance.
You can also demolish team fights. Hopefully, by now, you'll have finished
Nashor's Tooth. If not, please do so immediately. Without it, your ultimate's cooldown is 40 seconds. It should be doing around 900 damage (less, of course, factoring magic resistance). Doing more than that is great. With Nashor's tooth, your cooldown is 30 seconds. Pick up the golem buff, max out your Mejai's, or buy a
Deathfire Grasp or something (I usually don't buy one because I'm not close enough to use them, but I'm just listing an item that gives CD reduction).
During Late Game, if your AP has been growing well (IE you haven't been dieing and losing your stacks), you should still be strong enough to blast a few people to hell. You're amazingly cheap 24 second cooldown laser will help you with this. By now, you can just start to randomly fire it. Mow down creep waves with it (especially good when pushing), snipe off people for the hell of it, that kind of fun stuff. You can fire it at people just to piss them off. Who cares? You have the mana, and it'll be up again quicker than you can finish a Pop Tart. This is when Lux gets even more freakin awesome than before. Spam that baby.
Oh, and by the way, if you really, really, really have to get a last item because you have 5000 gold and the game actually lasted this long, buy a
Lich Bane. The AP is good, plus with the added passive, if you hit someone with a normal attack after hitting them with a spell, you can do some serious damage. I've only had one or two games where it got this far, however.
Summoner Abilities
Clarity This is quite a useful spell for Lux. She is a mana whore. She will eat your mana until later levels when you have both your normal, inherent mana, and the mana added from Tear of the Goddess. Even then, if you're been spamming your spells nonstop, then you can still run out (Yes, it is possible to suck a 3000 mana pool dry, especially when your cooldowns get lowers) It's useful in a pinch.
Teleport Teleport is an all out useful spell for anyone that doesn't already have a teleport ultimate (Lux would fall under that category). It's a bit of a long CD, but it can get you to where you need. Even if you're late, you can still zap them from across the river, from tower to tower, with your laser.
Clairvoyance This is a decent spell if you can't blind-shot worth a damn. I've had plenty of practice with Ezrael, so it's easier for me. The good thing is that there is such a short time between the red light appearing and the laser itself that it's harder for them to run, even if they see that eye. I don't use this personally, because it just feels so much more awesome if you shoot them when you can't see them.
Flash This spell is good if the other team is targeting you. It gets you out of their range, but close enough so that you're still effective. Otherwise, it's good for escapes, though you'll never really use this to chase because you have that laser.
Ghost Same as Flash, but this lasts longer. If you're taking an escape spell, choose one of these two. This is better for chasing, though if you can't kill them with your laser, then you really shouldn't be chasing with someone this squishy. You can also swap this out with teleport, because then you'll have a faster way to get somewhere with a low cd, along with an escape. I prefer teleport, however, just because you'll get in position almost immediately to throw your shield or to stun. Or to laser. Hehe, the laser deserved it's own sentence.