Been playing with this build for some time now and it seems to have been working for me so far. Its a good mid build and can be viable for bottom as well.

Ive picked ability power all the way with some magic pen. The quints are good for the start of the game to try to get that early kill.

I went for bringing up my ap as much as possible with the added utility we get extra mana, mana regen, and gold per 10/s.

We start off with lots of pots and some mana regen so we can use our spells to slowly peck away at the enemy. The we start off with some extra gold, and work towards mejais soulstealer. Works great for a snowball effect. With the shard of true ice we get an activated slow for the begging of the game till we get our ryjais staff. Once we get our items filled we can sell shard of true ice for another/better item. We have the hourglass which helps with some armor that we need. but accoriding to the build that the enemy team is we may need to change it for an void staff or an abyssal scepter, or the unholy grail(my choice).

Starting off with the Singularity is the easiest skill shot to land of the opposing lane players. Then a stun is the next one to get. Now for how to play this char early game. With lux passive she does extra damage with her basic attack after she has hit an opponent with one of her spells. early game this is a very good in the start of the game. try to get the enemy to half health and u can get a kill easily. When u get a stun run up close and the throw down the singularity the hit them with a basic attack and then activate the singularity again making it explode and putting lux passive on them again and then hit them with another basic attack and they should fall or at least make them go back. Final spark is a great way to catch low health enemies running away. But in mid/end game it can change a team fight in a different direction. More on this later. Later your can do a great amount of damage to a player with a quick stun throw down singularity ult then blow up singularity(great combo for great damage). Now your shield. It is very useful and will help alot. use it while turret diving. and at the start of team fights cause it does have a decently long cd.

Pros.

Great damage to all but tanks.
ult has very short cd.
good stun and slow for team fights/saving teammates.
good at the start of the game

Cons

low health, very mana hungary.
low survivability.
longish cd on normal spells.
all spells are skill shots.

At the start of the game we will let the monster buff go to the jungler. If no jungler getting blue at the beging can be very helpful. At lvl 6+ you should get the blue buff(hard solo at this lvl) despite is there is a jungler or not. At 12 you can easily get this solo. And if bot and mid lane are pushed but dont hesitate to go take their blue buff(no reason to let them have it). If you are pushed back and cant farm to much some jungling can work for you, like any person really.

Lux is great for team work and early game ganks. Playing mid you can help top and bot, which is great for turning the tide in your favor. If you have ult up with some health you can drop in and help other lanes. a quick stun singularity and ult can do great damage on a lane with minimal risk to yourself.

Now i said i would talk a little bit about my strategy with using lux's ult. Now according to how the fight starts out you will go in a few different directions. If you find both teams about to fight in the center lane send an ult down there and get some early damage in for the fight. With two buff and unholy grail cd reduction ur ult's cd is about 20 sec so it will be up when the fight is going on and you can use it when it comes off cd. now if you get jumped from in a bush stun, take a few steps away and then use ult.(with them being in a bush it is likely that you will hit most players, if not all. Trying to hit all players with her ult is very nice but dont wait to long to use it or you can lose players and the fight is over any way forest team fights are nice cause teams are in small places and easily you can hit all enemies in the battle.

Using ur passive early game can be a great benefit. Helping push other lane when mid is gone will be great. Using the ult at the right times can win or lose you the battle. So practice with the skill shots. get good at them and know your enemy priority. s