This is the build I've played with Lux for quiet a while now.
Precaution: Please briefly read at least the Items and Skill Sequence chapters before following through with the builds.

This guide is not finished yet, I accidentally published it because I'm dumb.

Pros:
Long Range
Lots of CC abilities
Will change the flow of any team fights on a dime
The infamous Finales Funkeln

Cons:
Squishy
All skill shot abilities

Greater Quintessence of Potency:
This gives you the great AP at the start, giving you a decent damage early game.

Greater Mark of Insight:
Gives you the magic penetration you need before you get your Void Staff or Sorcerer's Shoes.

Greater Seal of Force and Greater Glyph of Force:
These two starts to be better than the flat AP runes at level 6, right when you start to get aggressive and finishing off opponents with your Finales Funkeln.

The gist of it is this: Finales Funkeln > Lucent Singularity > Prismatic Barrier > Light Binding.

First point goes to Light Binding, This is for 4 reasons:
1.) Get enemies off your tail
2.) Immobilize enemies for easy ganks
3.) Do some decent pre-minion-spawn with Light Binding followed by an auto attack to ignite the passive
4.) Get an easy kill if enemy is ever stupid enough to attack you in the range of the tower at early level.

Next point goes to Lucent Singularity, from now to level 6, this will be your main tool to damage the enemy team, to use this skill effectivly, you must know how to predict the enemy's movement. Observe how the enemy reacts to seeing you cast the spell, because as you know, Lucent Singularity travels quite slow and is easily avoidable if the enemy is paying attention to Lux's animations. Normally people will run back towards the tower upon seeing you cast that spell, so you would want to place it behind them; Of course this does not go for all players, I've seen a lot of people goes to the side when I cast Lucent Singularity, so adjust your placement to that so it is in front of the path they are taking. Note: do not place the spell so it doesn't include the ground they're standing on, sometimes people arn't paying attention and just doesn't move, if that's the case you've just lost a free hit.

The third point goes to either Lucent Singularity or Prismatic Barrier, here's an easy way to determine:
1.) Are you laning with a partner?
2.) Are you doing somewhat bad in terms of health?
If you answered yes to any of those questions, you should take Prismatic Barrier.
Prismatic Barrier is a great shield, especially at early game. If you are getting chased, here's what you do:
1.) Prismatic Barrier you (and your partner if you have one) to prevent dying
2.) Light Binding the enemy chasing you. (should be easy as he's chasing you, not in weird angles or paths)
3.) Cast Lucent Singularity between you and the snared enemy to cut off his path (unless its Master Yi on Highlanders, then just run)
4.) If you are in a safe place, or the enemy is alone has low health as well, explode the passive, then Lucent Singularity, then the passive again.

From now on you want to focus on leveling Lucent Singularity, as it has one of the longest attacking range of all your abilities, and it should rarely miss the target. It is one of the best harassing tool you'll have, but don't rush to trigger the passive if your enemy is ranged as well, and has abilities to hit you when you get close for auto attack: It's not worth it especially if you're harrasing. Remember, You're very squishy and will easily be killed if the enemy gets a hold of you.

The next is Prismatic Barrier, this is great for team fights as it gives your team mates that few extra seconds to finish off their opponents. You should be able to shield your teammates twice or even thrice (yes, that is a word) with an average length team fight. It also gives you extra insurance when being chased.

And finally, the Finales Funkeln: This is where the Clairvoyance comes in.
As you know, many will stay next to their turrets and recall when at low health, and usually you can't see them with the minions and enemy champions in the way blocking you off.
Well, you just happen to have this super ranged, super damaging, super duper master spark 2000 to snipe people off and no sight range to use it!
But with Clairvoyance, you now can see anyone, anywhere on the map, so if they think its a good idea to hug the turret and recall, they better think again.