Why Lux is OP
First off, according to champion.gg, Lux is the second best champion in the game. She has the second highest win rate to Mordekaiser in Plat+. I'd like to explain why that is and why she isn't permaban.
http://champion.gg/statistics/#?sortBy=general.winPercent&order=descend
TLDR: Her abilities were overbuffed with 30% increased AP ratio, 33% increased damage and CC on her binding, 36% increase to the size of her slow zone, lower mana costs, and more reliable damage in the form of in-flight detonation of her AOE(similar to a Gragas barrel.) Her waveclear was also compensated by Luden's Echo along with assassins falling out of the meta. She's left unbanned because she's mostly poke and all skillshots which allows her enemies to blame themselves. Rather than champs who are melee like Fiora, Morde, GP, Darius, or Diana who have higher ban rates because they have fewer skillshots which makes players feel powerless.
Why is she so strong now? The buffs she's received over tuned her.
>V5.17: Light Binding.png Light Binding Mana cost reduced to 50 / 55 / 60 / 65 / 70 from 50 / 60 / 70 / 80 / 90. Secondary target will now receive full damage and snare duration.
Previously the second snare did half the damage and half the snare time. This increased the power of her binding by 33%, damage and cc. Even more importantly, it increased the second proc on her binding by 100%. Now, not only can Lux do more damage through a minion, but she can only land a full combo without losing any damage. This ups her lane damage and her overall damage across the board. Not to mention, prior to the buff, her mana costs on Light Binding were much higher which prevented her from spamming it so frequently.
>V5.12: >Prismatic Barrier.png Prismatic Barrier NEW EFFECT: Lux now gains her initial shield instantaneously instead of after the 0.25 second cast time. Lucent Singularity.png Lucent Singularity Slow zone radius increased to 350 from 300. NEW EFFECT: Can now be activated while in-flight to immediately detonate upon arrival.
This buff is for players with high ping. The shield and the 'in-flight' detonation allows player in high ping environments to do damage and self shield much faster. Overall it increase lane bully potential and damage prevention. It's difficult to quantify, but this was also a significant buff to her power. Even so, it makes landing lane harass much easier. The slow radius increase is quite significant. While it's, roughly, a 17% increase to the radius. It's also a -36%- buff to the total surface area her E slows.
>V4.13: >Illumination.png Illumination Damage changed to 10 + (8 × Lux's level) (+ 20% AP) from 10 + (10 × Lux's level).
This added an addition .6 AP ratio to her full combo if you account for auto attacks which increased her total AP ratio on a full combo by 30% if she's allowed to auto attack. Although, that's not bloody likely to happen, at the very least, it increased her full combo without autos by 10%. To put this into perspective, it gave her roughly the same damage as her previous passive early game and much more damage once she started building AP items in terms of lane harassment.
I want to stress how large these buffs are. When you see buffs of 33%, 36%, or 100% they're extremely significant. Most of the time you'll see damage tinkered with in the range of 10% to 20% maximum. Not only does she get all these buffs, the items have fallen into her favour as well. First off, a big problem people have had, this season, is the fact Lux can't one shot a wave with her E. Building a Luden's Echo erased this problem. Lux also has very low move speed and quite enjoys building an item to compensate that. On top of that removing the mana regen component to utility mastery is actually a buff to her laning phase. Low mana regen is much more useful on champs that have low mana costs than for champs that have high mana costs. If the mana regen mastery allowed a champ with low mana costs to cast two extra spells to Lux's one, it most certainly would most certainly out damage Lux's E. Not only that, because lower mana spells cost less mana, the enemy will be able to cast those spells more frequently.