Hello! I'm Ahrimu from the EUW server. I'm Silver 4 but I don't really focus in Ranked, I'm currently having 530k mastery points and +800 games on Lux! I'm making this guide for people that are new to Lux and want to know what's good and what's bad for her. I'm not trying to sound professional, I'm just sharing my thoughts and opinions. =)

Lux's Passive (Illumination)

After casting an ability on an enemy, that enemy gets marked for 6 seconds and Lux can pop that mark by auto attacking them, dealing damage.
Lux's Q (Light Binding)

Lux releases a sphere of light that roots the first 2 enemies/minions in front of her, dealing damage to them.
Lux's W (Prismatic Barrier)

Lux throws her wand at a certain direction, shielding every ally that passes by the wand. When the wand comes back to Lux, the shield power is bigger.
Lux's E (Lucent Singularity)

Lux fires her light to an area, enemies that step on that area get slowed and after a few seconds, that area explodes and deals damage. Lux is able to detonate that area before it explodes.
Lux's R (Final Spark)

Lux fires a beam of light in a straight line, damaging all enemies on that light and popping the Illumination mark.

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Lux's passive is really good for poking because you can do simple combos like:
* Q+Passive, in other words, you can root them and then auto attack them to deal some extra damage with your passive. You can also do this with your E.
* Q+Passive+E+Passive, this one is a bit more complicated because you have to do all of this while the enemy is rooted. So, you hit your root then you auto attack then you throw your E and you auto attack once again.
Other combos/tricks:
* Q+E+R, in mid/late game, this is what you have to do if you want to get a kill, your damage is gonna be so insane that you're going to delete squishies this easily.
* Q+Passive+E+R+Passive, in early game, if you want to get a kill, this is the combo you should go for.
* Q+E, this is a really simple trick if you want to survive from enemies chasing you. First, you should root them and if they're having Magic Resist to counter your root duration, you can use your E to slow them down and detonate it when they're not in the area anymore.
Lux doesn't really have a lot of combos but the ones listed above can be complicated to master (because you have to be fast)!

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In my opinion, maxing E first is the best thing you can do as Lux Mid because your E is pretty good for poking and wave clearing.
You can also max Q first but ONLY when your team is going to invade the enemy team's buff and they plan on getting a kill. If you end up not getting anything from the invade, you might lose some minions from your 2 first minion waves because you don't have your farming ability.
After E, I like to max Q so if the enemy decides to engage, I can use my Q+Passive+E+passive combo and deal a decent amount of damage.

Flash and Barrier

In my opinion, this is the best combination for Lux Mid because it provides you the escape you need (as lux doesn't have any mobility) and some protection from assassins and burst mages.
Flash and Ignite

I really don't like taking ignite, Lux has long-range abilities so it's normal for her to stay away from the enemy. Lux doesn't need ignite when she's too vulnerable to get close to the opponent she's facing. You might do well in early with Ignite but Mid/Late game...you're not gonna do that well because your ignite will be useless.
Flash and Heal

This combination is also alright for Lux. It provides you some mobility (flash+movement speed from Heal) and sustain during a fight. The reason why I don't take Heal is because if the enemy laner takes Ignite, your Heal won't be able to do a lot. Barrier's shield is able to deal with Ignite but Heal isn't.
Flash and Exhaust

You should take this when you're playing against an assassin like Zed or Talon, it reduces their damage and movement speed. Barrier is also good against assassins but Exhaust is also often picked against these matchups.
Flash and Cleanse

This is a combination that I honestly never go for. This is often picked against enemies with long-lasting CC like Ahri's Charm or Syndra's stun. It's obviously a good pick and you should consider taking it if you're not that great at dodging CC skillshots.
Flash and Ghost

I rarely see people taking this on Lux and I can understand why. This combination provides a lot of mobility but no protection for Lux. Is it viable? I don't think so.
Flash and Teleport

This is alright to take on Lux, but not in Mid Lane. Teleport is good for Top Lane Lux.

Now.. Jumping to the items!
Doran's Ring

Cost: 400 gold
Attributes: 15 AP and 60 Health.
Passives:
* +5 mana regeneration per 5 seconds.
* Basic attacks deal additional physical damage to minions.

As Lux, I always like to start with Doran's Ring because it gives you some Health, AP and Mana Regen. I don't really see other starting items that are this good for Lux.

The Dark Seal

Cost: 350 gold
Attributes: 10 AP, 100 Mana, 25% increased healing from potions.
Passives:
* Grants +3 AP per stack of "Glory"
* Grants 2 "Glory" stacks (+6 AP) if you get a kill and 1 "Glory" stack if you get an assist (+3 AP). Max stacks you can have: 10 "Glory" Stacks (+30 AP). You lose 4 "Glory" stacks if you die.

Personally, I don't enjoy buying Dark Seal as a first item because you just buy that if you're gonna get a lot of kills/assists. Even if it's an easy matchup and you feel confident, it's still not a good idea. Imagine if you get camped? Or if you understimate your opponent too much? It's gonna be a waste of gold. You can still build it (and maybe upgrade to Mejai's) if you're getting a lot of kills and you're sure that you're not gonna lose the stacks

Luden's Echo

Cost: 3200 gold
Attributes: 90 AP, 10% CDR and 600 Mana.
Passives:
* Extra 10% CDR (so that's a total of 20% CDR)
* Gains charges upon moving or casting. At 100 charges, the next ability damage will deal extra damage to the enemies hit by the ability and the 3 nearby enemies.

THIS ITEM! This is a must when you're playing Lux Mid. Yes it costs a lot of gold but it's worth it because of the attributes and damage from the Luden's passive that will finish off the minions/monsters.

Sorcerer's Shoes

Cost: 1100 gold
Attributes: 18 magic penetration
Passive:
* +45 movement speed

Most mages build this item because of the Magic Penetration it gives you. If you're in a matchup with no heavy AD/AP, this is a must. It's also really important against tanks/bruisers!

Rabadon's Deathcap

Cost: 3600 gold
Attributes: 120 AP
Passive:
* +40% AP

I don't really have to explain why this is a good item because it's so obvious. Imagine if you're having 500 AP and you decide to buy this item. You get +40% of your current AP so that means that you'll have 700 AP after purchasing it because 500X0.4= 200 (40% of 500 AP is 200 AP) so 500+200 = 700 AP.
WARNING! This is NOT a good choice for a first item, yes you're going to get a lot of AP from it but you're not going to have important attributes like Mana, Health, Cooldown Reduction etc...

Okay so...now I'll talk about which items you can build after Luden's.
Lux is a champ that can build most AP items and that leads you to a lot of different builds to try out.
Can I build Zhonyas? Yes, if they have an assassin like Zed/Talon/Kayn or if they have a lot of CC.
Can I build Void Staff? Yes, if they have a lot of Magic Resist or if they have Tanks/Bruisers.
Can I build Twin Shadows? Yes, if they have champions with a lot of Movement Speed (Udyr is a good example).
Can I build Spellbinder? Yes but I usually just build this item if I'm really ahead and I want extra damage.
Can I build Rylai's? Yes but I don't think it is that good because of the passive. You already have the slow from your E, why would you need another one? Doesn't work for me.
Can I build Rabadon's? OBVIOUSLY!!!
Can I build Morello's? Yes, if they have a lot of Magic Resist and if you need some HP.
Can I build Liandry's? Yes, if they have Tanks/Bruisers and if you need some HP.
Can I build Lich Bane? Yes but I'm not the biggest fan of this item because you have to use your passive a lot so you'll have to auto attack after using an ability to proc Lich Bane. Except for that, it's still a good item cause it provides a good amount of AP and it gives you some Cooldown Reduction and Mana.
Can I build Banshee's? Yes, if they have a lot of CC and AP.
Can I build Archangel's? Yes but I really don't like this item, you only get 50 AP from this item and Lux isn't THAT mana hungry for this. Big NO.
Can I build Hextech GLP? No, this item might sound really amazing on Lux but not really, The passive isn't that good because you already have the slow on your E. You can still try it out though, not a big NO from me.
Can I build Hextech Protobelt? No. In my opinion, it's one of the worst AP items you can build on Lux, you don't need the dash the active provides you and as a first item, you don't get any mana and Lux NEEDS mana in early. Not worth the gold.
Can I build Hextech Gunblade? Big NO from me because the item gives you 0 Mana, and as I said, Lux NEEDS mana. Building Attack Damage and Life Steal on Lux? Not the best idea, Lux isn't an Assassin. This item is not worth a try in my opinion.
Can I build Nashor's Tooth? No. I've tried this before and honestly, I don't get why people would buy this on Lux, attack speed just doesn't work for me.
Can I build Rod of Ages? Yes but only on Top Lane Lux.
Can I build Shurelya's? Yes but not in Mid Lane.
Can I build Guinsoo's? No, that's just a terrible item for Lux.
So yeah, items with Attack Speed, Attack Damage, Life Steal and No Mana are a NO for me.

For Lux Mid, these are the best runes. Sorcery 1st path is really good because it gives you mana (Manaflow Band), cooldown reduction (Transcendence) and some extra AP (Gathering Storm) and also because of Comet (really good for poking). Inspiration 2nd path is also amazing because you can get Stopwatch (Zhonya's active) and some Cooldown Reduction. You can take both Comet and Aery though, you can proc Aery more easily (with autos) but the damage isn't the same and Comet deals more damage but has a bigger cooldown.

I see some people taking Dark Harvest on Lux and I don't really get why. I've tried these runes a couple of times and I just don't enjoy them. Domination 1st path is so weird for Lux because it doesn't provide you the stats you need, Ultimate Hunter is the only good thing in the Domination path. Sorcery 2nd path is completely fine for me. Dark Harvest didn't really make a difference in damage for me when I played with it. It's worth a try but I don't really enjoy it.