This is my first build, I am not currently in the ranked teams yet, but this build has brought me to victory many times and it will help you too. Please leave constructive comments ^^

Pros:
High burst and harras
Easy to gank with
Many escape mechanisms (q snares, e has AoE slow)

Cons:
Mega squishy
Team has to ss every time for you to survive
Is dependent on kills, no kills is no lux

They explain themself really, lux needs mana regen, not max mana

I find that the extra health, doesn't ever save me with lux, while the extra mana regen helps me very well early game to get fed. instead of increased buff duration you could go for biscuiteer, for even longer sustain early game, your choice. Also, the reduce recall, highly underrated, this will give you extra time to farm every time, and give you an edge over your opponent after every kill/recall a must have for lux

just build them in that order, if you feel you lack speed, pick up some boots with some spare gold before you buy the super expensive items. Follow this build and you could be looking at a cap AP of about 830+ that is over 1100 damage with a big range ult that only has 24 sec cd!!

Lux snowballs into a mega poker, upgrading q and e to max asap is a must, as for your shield, you wont need it until late game, if you would need it, it probably wouldn't have made a difference

Flash, for obvious reasons.
Clarity, this baffles my teammates every time, but there is method in my madness. Why take ignite, if i can deal extra damage with my q and e from mana i just recovered with clarity? ALSO, this is a great way for baiting, for example. You are poking teemo to the next world, until 'suddenly' you are out of mana, and he has 250 health left. What every teemo would do, is bully you. Use your clarity, ult him and you have a kill! Simple. So that is why Clarity helps, it also helps you sustain lane even longer, big lane sustain is big minion feed.

And that is it for my first guide ^^ Let me know what you think ^^