Just A Few Notes

This is an ARAM build for the Champion, Lux. It also works with Summoner's Rift, however I don't use it as often there because it is very APC heavy.

The lane is classified as "Middle" because it's ARAM- All Random All Middle.

Start with going for Morellonomicon.

Lux relies on mana, and this build does not use Clarity. Why? Later on in the game, Lux will not need it because of the 400 extra mana and extra regen after building Athene's. That is explained later on though.
This early 20% CDR is beneficial as well, and it also restores 20% of your max mana upon getting a kill or assist. Due to her E skill being an Area of Effect skill, assists are not hard to get.

Begin Building Luden's Echo next.

This item is helpful because of its passive, which damages others around the area where the last spell was cast. Believe it or not, I have actually managed to snag a few kills this way because of unsuspecting enemy champs feeling safe when standing near but not in my E skill at low health.

Rabadon's Deathcap

At this point you should have 200 AP, maybe more depending on your rune/mastery set. Start building Rabadon's Deathcap third. This will help you mid game with an AP advantage with the 35% AP increase as its passive.
Some may buy this first, but these people tend to have less escape routes. Their mana will deplete faster and while they have higher AP in the beginning, they can't use their skills as much. Clarity may help, but it also has a recharge time.

Fourth Item: Zhonya's Hourglass

Lux often finds herself in a bit of trouble when trying to escape a sticky situation. Building this item will provide that extra bit of CDR to keep the snares and slows going, as well as the active skill to become invulnerable for a few seconds. This also gives some armor which can make taking hits from an ADC a bit easier.

Almost there! Build Void Staff Next

Okay, now Lux is becoming a worry to the enemy team. You may find yourself as the villain of Garen for quite a while. The enemy team may start building defensively to tank Lux's ultimate or any of her moves. They all hurt!
This will help neutralize their efforts with 35% MR penetration.

Final Item: Athene's Unholy Grail

This is your final item. Athene's Unholy Grail will provide extra mana regen to be able to spam abilities and fire your ultimate every minute (literally, it's less than that at this point). While Lux is APC, her shield will now heal those it hits when Athene's has charges. This keeps team fights to your team's advantage, which is also helpful because those teammates will be taking most of the damage for you.
Note: if the enemy team is aggressive, build this item earlier on. I would build it right after or right before Rabadon's if this is the case.

Alternate Build

Replace Athene's with Archangel's Staff

Build Archangel's Staff first, before Morellonomicon. This will give you charges on your Tear of the Goddess for it to upgrade to Seraph's Embrace later on.
Seraph's Embrace also as an active, which nobody seems to realize. This gives a shield which actually tanks for a number of damage. Escaping is easier when this is active.
Also, while this only has +80 mana, the "Awe" passive is in effect. "Awe" grants 3% of your total mana as AP damage. When this is fully maxed at +1,000 mana and Morellonomicon is built, that is 1,400 mana not counting leveling. This item now grants +124 AP (80 + 42) which is a little better than Rabadon's without its passive.

Replace Void Staff with Liandry's Torment

If nobody seems to be building items that grant defense against ability power, or you need some extra health, build Liandry's Torment for it's +300 health. This also grants a passive which burns enemies for three seconds. Using this with Lux's E skill can double the damage of this passive with the help of her slow.

No Boots?

I find that using Lux's rooting and slowing is fine enough to not need the extra movement speed. This is also why I take heal instead of clarity, which I can further explain in the next section.

Heal

I take heal because it's extra health that can save Lux while running away or healing herself and an ally in a team fight. This also adds a 30% movement speed briefly, which assists in escape.
Personally I am not a fan of barrier because of its lack of MS bonus. It is definitely a good alternative for those who like it better than heal.

Flash

Flash is almost a must-have on any champion, which is self explanatory. It is reliable to dodge an ultimate shot, secure a kill, escape being killed, escape from a tower dive, etc.

Pros:

--> High AP damage
--> Good against tanks with burn or magic penetration
--> Gives decent health and armor
--> Actives (depending on set) include a barrier to tank damage while running (or in general) and an invincibility for 2.5 seconds.

Cons:

--> Magic resist is very low, armor is pretty low. This means being targeted by a champ with high burst damage is an extreme concern.
--> Without spells for an aid, escaping is still not the easiest because there are no boots for the extra MS.

This is my first recommended build I have written. If i missed anything feel free to let me know in an non-aggressive way! We all make mistakes, and I love reading about what I can improve on, and how this build worked for you!

Thanks, and may Lux light your path to victory :)
-Fusionfang
December 31. 2016