The basic idea of this build is to take Lux's passive to a new level.
We take Q first, so we can trade with HOB level one.
Our playstyle with Lux is a bit different with this, as it requires us to spend a fair amount of time in auto range, and weave those auto attacks in with abilities in order to repeatedly proc spellblade.
A basic engage will begin with Q or E, Proc Passive, Auto, Proc hail of blades, Proc spellblade, Hit for a couple autos, then throw a W to proc Shield Bash and Spellblade again. Then you can Finish with Q/E/R. Its really pretty versatile. You can pretty much spam abilities and get lots of procs, but being mindful of spellblade 1.5 second cooldown is also important especially in the case of W. If the enemy is fighting back, you aren't in a hurry to throw W anyway since you will initially be Safeguarded by crown and bone plating.

This is probably not the best way to play lux, but its fun and enemies won't expect you to run at them like a bruiser, causing them to misplay or misunderestimate you.

=====EDIT FOR S13=====
With ravenous no longer giving omnivamp, that option can no longer be justified, even if you are very ahead.
XXXXRavenous also synergizes with Riftmaker in giving a good deal of omnivamp, and acts like a bootleg Ludens. XXXX
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I came up with this idea after accidentally getting into a game with Tristana Runes and trying to find a build that synergized with them. I ended up stomping the lane by running at the enemy and autoing them like a crazy person, much to their confusion

Late game, lux is probably better off building the meta and throwing Q's from max range, but this build gets you to keep taking advantage of her passive while getting into the fray in a fun way and can be viable if your team can provide additional shielding and blocking.

You're still Lux. You still do Lux things. You want to be paired with champions that can chain your CC or capitalize on it, be they immobile bruisers that can run in and bash slowed and rooted enemies, or ADCs that can obliterate rooted tanks.

What you don't want on your team, are champions with displacement abilities. There is nothing more frustrating than missing a Q because Sett does a facebreaker or Swain pulls them in.

Ultimately, your threats with this build are the same as they are with any other Lux build. What this build does is give you some flexibility with sustained damage output and durability. This can be used to soften the threats from certain enemy champions, like Katarina.

Ultimately, what this build does is sacrifice a bit of artillery power for durability and ability haste. As a result, you are safer to be more aggressive in lane, and have more survivability and therefore, utility, in team fights.

Consider this build any time you know you are going to end up dueling in melee range with your laner. Consider this build when the enemy team is heavy on melee bruisers. Also consider this build if you're going up against another artillery mage, such as Xerath, as you can behave in a manner nobody expects from lux and force out of their comfort zone and into your game being aggressive.