Lux kinda sucks. If you ask me, here's why.
Her early game play pattern holds up, but her later stage game patterns are pretty trash.
Passive: Some passives are designed to scale. Some passives are designed for the laning/farming phase. There's nothing inherently wrong with a passive that's not as easy and fluid to use in later stages of the game, but the way this is done on Lux sort of adds to the problem.
Q: The attack snares 2 dudes. Move's kinda floaty. Once again, on its own, the move isn't the worst of things.
W: Allied skill shot that shields people. It now shields with double power on someone you shield twice. This move has the MOST issues.
E: The attack targets an aoe and slows the area, then hurts. Perfectly fine spell.
R: A thin, long, high damage nuke (insert Lenny face here) on a low cd. This is where our troubles begin, so to speak.
So here's where we run into issues.
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Lux's passive has a "Deathcap Syndrome" sort of problem. The fact that it is/can be applied to any rotation of moves means that the value of those moves has to be shot a bit to leave room for up to 3 separate passive procs. Lux's numbers without these procs aren't amazing, but WITH them they're a bit uncanny. You may have instances where you can get 2 hits of it off in lane, but after lane, a lot of potential damage output is locked up here.
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Lux's W is way too slow on the return. As an artillery mage first and foremost, why is her W so bad for reacting to quick engagements on her? Buffing her potential shield power is nice and fun, but that pushes her towards bot lane more than it makes her mid lane game better...similar to how you can now see a bunch of pros trying Lux support on probuilds now (some of them building COIN might I add (NERF THE GOLD GEN)).
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Lux's only damage move that doesn't have utility effects...is her ult. This justifies making THAT low cd, but it also means there's no way to justify giving her more up time via giving Q or E more spammable cds. In later stage team fights, Lux is basically non-existent after she uses each spell once. W? Long cd. Q? Long cd. E? Long cd. Ult? Short for an ult, but it's STILL basically once a team fight.
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Speaking of that ult one more time, that 50% cd on kill buff kinda sucks. Like, what LoL team fight lasts even 15 seconds? Sure, if a few manage to scramble + you killed someone via ult, you could see them again in a bit while sieging or whatever and THEN we might be a tad grateful, but in most cases your team's already around to back you up for that type of scenario. There isn't many times you could say "Yeah, having ult up again after we won that team fight is really helping me now". Most you can do with it is shove a lane a bit.
All in all, with Lux's poor up-time, she goes from being pretty strong in lane against most non-assassin opponents to falling off a cliff Pantheon-style. The issue isn't necessarily "Lux's damage output is bad" more than it's "Lux's presence as a damage dealer is bad". Lux's damage output goes flying straight into shields, heals, tanks, damage mitigation mechanics...whatever, and when that happens, she's a sitting duck, waiting for her floaty ass W to get back to her corpse because Zed killed her before it even started turning around.
Long story short: Lux's cds are way long and her W is geared towards support, not mid. Her passive is a gift/curse that helps her early on only to screw her over later.
slows roots and stuns are our only "kiting" mechanism.