Hey man, I'm a Lux main (as are most people down voting or shit talking) and have played MANY games with her. I even have a famous guide with her. My point of telling you that is I have plenty of experience with her, and I almost know her like the back of my hand. I didn't downvote your post because she can be frustrating to play against. Her ultimate at level 16 with 45%CDR is actually a 27.5 second cooldown, while being around 30 with 40%CDR. However, she isn't op whatsoever, even though it might sound like it. She doesn't need buffs or nerfs per say, she needs CHANGES. I agree with you about her E and how hard it is to dodge. Her E needs to (in my opinion) be actually BUFFED, but have a smaller hitbox. This will give her great wave clear against the caster minions, but she also isn't able to freely farm and poke unless you are standing on top of the minions when she throws it. It will also make the spell much easier to dodge. Her biggest downfall is wave clear because right now, she is forced to E the caster minions, and then auto them to get them. This is where the enemy player can take advantage. Lux's E is on cool down because she just used it and she needs to walk up to auto these caster minions. There's the enemy's perfect chance to trade with her- and win. Lux only has her Q, and even if she is able to Q>auto you, your trade should do wayyyy more damage.
As for when she hits you with her E, you should be backing off if you have the illumination passive on you. OR, you need to harass her back. If I am playing Ahri and Lux E's and runs in to auto me, this gives me the perfect chance to charm, Q, W, and do EVEN more damage to her! I would most definitely win the trade.
As for melee champs, they get MR per level as a result. You also mentioned short ranged mages. The first one that comes to mind is Annie. Yeah, Lux can poke Annie down, but one Flash/Tibbers with ignite, and Lux is DONE FOR.
If she was op, she would be played in the LCS and would have way higher win rate. Last time I checked, her WR was 46% (in higher elos, I'm sure it's like 49% in bronze/silver).
She does do tons of damage, but in return, she has awfully high mana costs and a little higher cooldowns. Her E costs 130 mana at rank 5 and her 3 basic spells are higher cool downs compared to some other mages. She also has tons of weaknesses. Her shield got gutted, so it really doesn't help her at all. Level 1 shields 50 damage, a mages auto can break through that. She is very squishy and any assassin can whoop her. Not to mention, ALL of her abilities are skill shots. This is why she isn't seen/has a much lower win rate in higher elos, her spells are easily dodgeable and people in higher elos are normally better at dodging! Let's also look at the fact that the meta is now movement speed, meaning it's even MORE easy to dodge her spells. She can't combo you unless she hits her Q in mostly all cases (unless she E>R's you but that can be easily dodgeable/flashed away/dashed if your champion has one, or maybe you are CC'd by something else), but look at the items you can buy. As a mage, Zhonya's her combo and then jump on her. Abyssal is great as well. As an ADC, QSS is the best, just use it when she Q's you and then move sideways and auto while she misses the rest of her spells and auto her to death. You can even ctrl+3 that. Hex drinker is a cheap item for what you get and is very good early on in lane if you are laning against her. Finally, Edge of Night. Blocks that Q or E poke easy! As a support, Mikeals is amazing versus Lux and shield-y/heal supports saves lives, plus items like face of the mountain and locket of the iron solari. Lux has TONS of counterplay. I could go on about it, but I don't think nerfing her is the best solution. I can't exactly call out on WHAT to change because I'm not apart of Riot's balancing team, but I do know her Q is fine. It binds two people for a short period. I know people say Lux's Q>Morgana's because Morg's hits one person, but comparing those two is eh and Morgana's also binds for a VERY long time as you level it up. Lux's W needs to be changed SOMEHOW because the shield sucks, but just buffing the base shield strength will make her OP by her shielding her whole team by that newly high base damage amount. Her E does need a smaller hitbox, like I mentioned above. Her ultimate is actually in a good place right now, I'm not sure why they are buffing it- maybe for her not as good lategame (most Lux mains aren't too happy about the buff coming up because Riot could have done better, but it is a buff so we can't complain).
Anyways, those are just my personal opinions and I hope this gave you a little different perspective coming from someone who fully understands Lux and isn't just like "IM A LUX MAIN SHES THE BEST BUT SHES NOT OP SO DOWNVOTE!!!!". This post wasn't meant to bash on you or anyone else that feels this way, I am just hoping to maybe give you some insight on what others MIGHT be thinking (and definitely what I'm thinking), without just saying "this sucks, downvote" and moving on like others did :/. I respect the fact that you posted your opinion, even if people didn't agree with it! And I do agree with you upon certain things! GLHF! (and sorry for the long ass message)
-Luxeøn
From 7.1 to 7.5 she has barely had a 50% winrate. I know her kit may seem broken but its really not. All of her abilities are very predictable as her Q and E are actually pretty slow. Her ult is a straight line with a red indicator, everyone knows not to walk in a straight line when playing against a lux. Lux is like Lee sin, she is pretty strong before 20min but after that she falls very hard compared to Morgana. Lux is pretty balanced, I think you just need to dodge more lol.
