Lux needs some love
I have been playing Lux as my main since the first year LOL was released. She was once overpowered and nerfed to balanced. However, with so many new mobile champions becoming the meta, Lux is hardly viable in competitive level. She excels in team fight, which is totally fine. The worst part is her laning phase. Her ability to wave clear, roam, harass(yes), escape, and snowball is inferior, especially during early game.
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Wave clear Her wave clear is slower than most mids. Zed, Yasuo, Xerath, Katarina, Orianna, Sydra, Lissandra are played by me a lot. These are all frequently played champions recently. Some of them don't even spend mana. Lux cannot wave clear fast enough to keep minions out of turret range facing most other mids. In addition, her mana depletes rapidly if spells are used to catch up wave clear, and that is still slower than most others.
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Roam Lux has no mobility. She has to walk to other lanes without acceleration, blink, dash, or teleport. The opponents can react fast enough even without any wards in the river. Mid-laner responds for ganking top and bot when you try to carry the team. Lux has no presence that causes significant threat to other lanes. Not to mention the wave clear problem which costs her waves of minions for an attempt of difficult gank which is likely to fail. Lissandra and Xerath may have the same problem. Their skills are much easier to land compared to Lux. Plus they can wave clear efficiently even with no strong items.
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Harass Lux cannot harass frequently before getting her Charlice. Even if she has enough mana, her poke is easily dodged or mitigated. All spells that provide mobile spells, shields, healing can mitigate her damage due to her long cooldown. She doesn't have a poke as reliable and short cooldown as Orianna and Syndra, who don't have any disadvantages of Lux listed in this post.
The range of her E is also problematic. Non-mobile champions like Xerath, Ziggs don't even have to get close to poke. They don't have to worry about missing Q once, because it's up again after a few seconds. Yet it's easier to land and deals more damage. Considering how slow the projectile speed of Lux's E, any experienced player can side step dodge effortlessly. The only way is to make it effective is to stand closer to reduce the travel time. This would however put her into a very dangerous risk against assassin mid, and gank from enemy jungler. Besides, even getting closer to non-assassin mids is impossible against champions that poke you miles away. Think of Xerath, Ziggs and Syndra. You have to take a bunch of damage before having a chance because Lux has to literally WALK towards them. The only strategy is try to hit a Q magically so then you can land your E.
I still remember the time where Lux was considered the unique poke mage. Now, there is a bunch of other champions that poke in a much safer distance and reliable hit rate.
I believe there are some possible changes that help her a bit.
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Increase the projectile speed of her E. It should make her poke much more reliable, or;
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Reduce mana cost of E. To compensate for the shooting average, or;
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Double her second shield amount if it hits only her. Not changed when a teammate touches the shield. It should help her survivability against mobile deadly assassin.
TL:DR: Lux's team fight is great, but her laning phase sucks too much, preventing her from growing strong enough to be relevant in team fights. Bronze and Silver are the only places she shines because no one dodges skills anyway.