Not Updated For Current Season
This is how i play Lux as mid. Its a stable build, maybe a little slow on AP but it will come. One of the things you need to look out for, is the early game, you are really squishy, but as soon as you have catalyst, hp itsn't what you have to care about the most.
For runes: personal i take magic penetration marks, mana regen seals, flat or per level, as you like. And cooldown reduction glyphs, flat or per level, again dependet on what you like the most. Quints 1 movement speed, i found out that its quite nice to have movement speed quints. And 2 cooldown reduction quints, Lux have heavy cooldowns on her spells so cooldown reduction is a most, if you want to fire more than just 1 spell combo in a team fight.
I rush catalyst because you need the mana and hp regain per level as mid, it also makes you less squishy. Tear of the goddess, Lux is mana hungry as hell, so more mana is always good, it makes you far more usefull, it also prevent to from going back all the time, if you still are in the laning phase when you buy it of course. Rabadon's deathcap every AP carry's must have item, increased AP by 35% and 155 AP from the item alone, is never bad. Lichbane more movement speed, but also due to her passive a basic attack on a illuminated target is a good idea, it raise you damaga output really much when you have an Item like Lichbane. Another Archangels, more ability power doesn't hurt anybody but your opponents.
I use Clarity to stay in mid with mana longer, so you can push more and also prevent you from loosing exp by going back to refill your mana pool. Flash, is a great escape spell, but you can also use it offensive. Flash over minions so you can set up a good binding.