Lux is one of the first champions I ever played and is one of my favorite champions. I don't see her played as much as other champs like Nidalee, or Vigar. Lux has one of the shortest ultimate cooldowns in the game, and no one said it cant be as deadly.

Using lucent singularity early game helps keep the opposing champs at bay, as well as farming. Also Light Binding keeps you alive from ganks as well as sets them up for your team. Prismatic barrier doesn't actually do alot to help your team until later game, but in a pinch, every little bit helps.

Lucent singularity: shows you a area for 5 seconds and slows every opposing unit in it. Its lux's longest range ability, as well as largest area, and is useful in both team fights, and wandering the map.

Maxing light binding second gives your stun a punch, so it really helps start a team fight and hunt down champs who are running away.

Prismatic barrier is the last ability you need to max because as shields go, its not really good, until later game, when you have more AP.
Naturally, finales funkeln is to be upgraded as soon as possible. In the build this will have a 24 second cooldown so late game you can shoot it to start fights, as well as pick off survivors.

Early game, Dorans Ring will give you enough power to poke your lane opponent. Its important to get Boots of speed sooner rather than later, any move boost will keep you moving to avoid skill shots and out run ganks.

About the time you can afford Kage's lucky Pick, is about when I consider it mid game. This part of the game makes you more dependent on turrets and allys, than a flat AD build. Ionian Boots of Lucidity give you the cooldown reduction that lets you spam your skills keeping opponents in place and keeping the from escaping. Building Morellonomicon gives you the rest of the cooldown reduction you need as well as a lot of useful mana regen and a good chunk of AP.

By the time you have another Blasting Wand, its about the start of late game. Opponents are starting to get defensive realizing that you are an unstoppable powerhouse with a quick trigger finger, so you start getting Magic Penetration to tear them apart! From here, the more AP the better. You have all the cooldown reduction you need for the 24 sec Cannon and Magic Penetration from your runes, masteries, and void staff.

From this point in the match you have 2 choices, Archangels Staff or Rabadons Deathcap. This is all about the situation. Does the game look like its going to end soon? Go Deathcap. If you go deathcap first, you get all the AP you need to finish the match quick. Does the game look like its gin to go on for a wile? Go archangels staff.With archangles first, you get more mana and regen. Plus 3% of your mana, turns into AP for you. Also with Archangels, the new item patch gave it a boost. After you get all the free mana from the staff, it upgrades into a more powerful Archangels called Seraph's Embrace that has a nice mana shield active ability thats handy in a pinch.

For maasteries, I get 21/0/9. Focusing on AP, Magic Penetration, Mana and Mana Regen as well as Buff duration. This helps you deal the most magic damage possible. For Utility, the mana and mana regen help keep you going in a long fight.

Quints:
I have a special place in my heart for AP per level Quints. They help great amounts in the late game helping melt faces faster.

Marks:
Getting Magic Penetration Marks helps you later game when champions start to build their defenses. If they get Magic Resist, combined with void staff, helps to keep you doing lots of damage.

Seals:
I get Mana per level seals to help later game. The mana boost not only gives you more mana, but it will also give you more AP from Archangels Staff.

Glyphs:
I get AP per level glyphs, to help damage output late game.

You have to be careful early game. Being Lux, you are very squishy, so always be alert for ganks, Stun and Run. Dont be afraid to use the turret as a weapon. Slow champs with Lucent Singularity and stun them with Light Binding. Before you detonate lucent singularity auto attack the champ so your passive does bonus damage to target champ.

At this point, you function less like a damage dealer, and more like backup. At this time you can do damage, but you should know never go in dangerous areas alone. Stay by turrets and other champs, letting your light binding as well as Lucent Singularity to keep champs in one place so you can escape with your ally, finish them off, or wait for backup.

When in team fights at this stage, save finales funkeln. until after the fight. If they are running, you can pick off the survivors easily, or if you are losing, it gives your team a chance to get counter attack (if possible)

By late game, teams are running together in packs. You dont need to worry as much as long as you stay with a group. One of your jobs is to start team fights that the opposing team aren't ready for. Look for squishy targets that walk on the edges of the group, and stun them with your "Q". Your team will normally move to attack and in reaction, the opposing team normally trys to move to defend this stunned champion. Make sure you throw your "E" into the opposing team, aiming for the squishier champions like Ezreal. Also remember to use your "W" and try to hit as many alleys as possible. By this point, you have enough AP for your shield to work effectively.