I think this guide could use improving.

For one, your skill sequence is "unachievable".

You should never use Clarity in game. Controlling mana usage takes practice, but you'd need the slot for other spells like Flash or Ignite.

You shouldn't have a full item before buying any boots, considering Lux is really squishy. You will need the speed to escape.

Change the name! If you're going for AP Lux, say so.

Using E to farm lane is a TERRIBLE idea. The mana cost gets quite large when you max it, and it wasn't cheap to start with.

By late-game, the Ultimate should have a short cooldown. You can use it to initiate, AS WELL AS clean up.

NEVER KILL STEAL WITH YOUR ULTIMATE!!!

Laning combo: Lux and Soraka simply doesn't work. Not in competitive play. You'd be lacking Ranged AD DPS Damage. Will of the Ancients isn't such a good idea for Lux, as you shouldn't be getting hit in the first place. With the cooldown CAP of 40%, the lowest possible cooldown you can achieve on your ultimate is 24 seconds. 15 seconds = hacks. If you're going for Mana Manipulator, consider practicing to control your mana usage. You don't have infinite health and mana..Even Soraka has limits.

Baron stealing: The ultimate only takes half a second to charge.

Lux's skills have long cooldowns (Compared to other AP Casters), so use your skills accordingly.