True AP Carry's tend to be hard to play in dominion. You need CC to keep the bruisers and assassins off of you long enough to kill them. When you are squishy people will not hesitate to dive you on the capture point. Lux is by far my favorite AP to play in Dominion because she has a snare, slow, and shield plus she can dish out some nice burst damage.

Keep in mind, this is a Glass Cannon type build which requires some skill and experience in positioning, skill shooting, and kiting. I don't like the survivability builds on Lux or any AP carry for that matter. You lose a ton of your burst damage and end up just becoming a support because your damage is low.

Pros:
Nice burst
Long Range
Kiting ability
Ability to support team mates with shield as well slowing/snaring escaping enemies.
IMA FIRIN MAH LAZAH!!!

Cons:
Squishy
Susceptible to melee champs with gap closers when her cd's are down.
All abilities are skill shots

Start with Prospector's Ring and Boots. The ring gives you the most bang for your buck for that team fight in the beginning at top tower. Boots obviously to get there faster.

As soon as you have 700g go back for Ionian Boots of Lucidity CDR is important for Lux especially in dominion. After you blow your combo (Q-E-R-Pop E) if the enemy doesn't die you will need to kite until you can Q and/or E again.

Lux is very dependent on stacking Ability Power quickly her early game is rather weak. So next you rush Rabadon's Deathcap After this is built your combo will kill the squishy champs and severely injure the tanky champs so that they will either retreat or your allies will finish them.

Since Dominion games tend to be rather short I go Lich Bane next. This item has amazing stats apart from its passive buff. Magic resist, move speed, mana, and ap. Then there is the passive where your auto attacks will do around 600 dmg. You should already be auto attacking enemies in between casts because of lux's passive unless you are unleashing a burst combo where you don't have time to.

Should your game last this long then go Void Staff or Zhonya's Hourglass I tend to go void first bc its cheaper and the game is usually about to end soon and it gives a good boost in dmg especially to tanks.

Morello's Evil Tome is extremely popular on Lux and it does have strong stats on the surface. Decent AP, high regen, and very high cool down reduction. The reason I dont get it is you would have to buy it after Rabadon's Deathcap because it is your most important item and has to be rushed first. At this point in the game you dont need that 12 mana regen and Lich Bane is a far larger increase in your damage output.

If you are the kinda Lux player that prioritizes CDR over all else then I recommend Deathfire Grasp. Same stats as Morello's Evil Tome just a little less however its active is extremely strong especially against tanks and adds another devastating spell to your already OP combo. With 15% from Ionian Boots of Lucidity and 15% from Deathfire Grasp and 4% from masteries you're left with 34% cdr. Now all you need is an Elixir of Brilliance to max your cdr.

Illumination

Lux's passive is very nice for poking and harassing as well as last hitting minions. Every time one of your abilities hits a target they are left with a debuff. Once you auto attack them it ignites the debuff dealing extra damage. This coupled with Lich Bane passive later add a significant amount of dps to Lux's already high damage burst.

Lucent Singularity

Max this first. Very versatile spell. Can be used to slowing enemies, clearing minion waves, poking and harassing enemies, even checking bushes and around corners for enemy champs because it gives you vision. This is your main damage ability not counting your ultimate.

Light Binding

Max this second. This also deals a good amount of damage but its main usage is for the snare. Very powerful snare and can affect 2 enemies which means you can unleash your full combo on 2 enemies standing close together. Travel time on it is rather slow and can be hard to hit with especially from a distance. Sometimes its easier to throw your Lucent Singularity out first in order to slow the enemy and make it easier to hit with your Light Binding although i prefer to try and catch them off guard or bait them into chasing which makes landing a Q a lot easier.

Prismatic Barrier

Max this last. Can be a very strong shield once its maxed and you have a lot of Ability Power. Also if used correctly can shield your entire team. I use it to save myself and my team mates when they are low on health otherwise i focus on damage. If you want to play a more supporting role then max this second after putting 1 point into Light Binding

Finales funkeln

Grab this whenever its available. Amazingly strong ultimate and can be a game changer in team fights when you hit multiple enemies. It also ignites your passive Illumination so you always want to try and hit with Lucent Singularity first. Although if you ever find a perfect time to use it and hit 2 or more enemies dont waste the opportunity just to get your E out.

At the beginning I like to call mid. After you're done capping mid use ghost and join the fight for top. Hopefully your team isn't terrible and they aren't getting destroyed. When you get there hang at the back of your team and shield them with your w Prismatic Barrier. Then throw out your Q Light Binding on whoever you guys are focusing and E Lucent Singularity. You can use your E as dmg or as a slow. However the cd doesnt start until you pop it so keep that in mind if you want to use again soon. After top is capped and the enemies are dead I usually stay to defend while the rest of the team B's to heal up. Since I stay at the back of the fight and at long range I usually have the most hp left at the end of the fight.

Of course everyone has their own strats for dominion this is just how I like to do it. I prefer hanging around top and defending it. I'm able to hide in the bushes just above the tower. When an enemy comes to cap it i toss out my combo on them (which you can hit with all 3 abilities because of her long range). If you dont kill them and they chase you you just kite them around the bush and try to work your way back onto tower so you have the added dmg of the tower.

The ideal way to use lux's combo is to cast Q to snare up to 2 enemies. Toss out your E on top of them then start casting R. During the delay you can pop your E before R blows their **** up. You have to be quick b/c they will dodge your R otherwise. If they have Mercury's Treads you may need to skip the E and go straight to R b/c the snare will wear off.

The runes I choose are my basic set up for all AP Carrys. Magic pen to counter magic resist. Mana regen for the times you are stuck defending a capture point and cant B. Then AP for more damage. Movement speed Quints are also a great choice.

Once again a pretty basic AP carry set-up tailored for dominion with improved ghost, move speed, and reduced death time.

In dominion speed is king so improved Ghost is important for interrupting caps and kiting. Flash is just OP and should always be used because of its versatility.

My first guide so any criticism is welcome and feel free to request any info and i will do my best to add it.