I'm a Lux main, I really see her as jack of all trades. I doubt I'll be able to change your mind (haters gonna hate amirite) but I'll try anyway.
So, Lux's early game is pretty weak. She's gated by low base damage, high cooldowns, and high mana costs. Her E is not a good farming tool until she gets a few ranks into it, it starts with only 60 base damage (+60% AP) for 70 mana. Especially with the recent mastery tree changes, this means early game you'll be going oom quickly.
This low base damage is mitigated her passive letting her do some extra damage to targets she's illuminated with an auto attack. However, she has to get withing 550 range to proc her passive, often opening herself up to big damage from her enemy. There are quite a few enemy mid laners that you just can't proc your passive on, getting that close will end up with you taking more damage than they do. She can use her W shield to help with this, but again, the high mana costs ensure she won't do this more than once or twice without being completely oom.
Her Q is similar to Morgana's Q, except that it does less damage (60 / 110 / 160 / 210 / 260 (+70%AP) vs 80 / 135 / 190 / 245 / 300 (+ 90% AP)) , the root is shorter outside of rank one (Lux's is 2 seconds at all ranks, Morg's is 2 / 2.25 / 2.5 / 2.75 / 3). Hardly what I'd call OP
Then there's her ult. Obviously this her most damaging ability, with crazy range and relatively low cooldown. The reason for this imo is that it makes up for her only having two damaging abilities, with low base damage on them both. Yeah, if she gets to Q-auto-E-R-auto it's going to hurt really bad and oneshot some squishy people mid-late game. This is the same for every mage. If Vel'koz Q-W-E-W-R it will do the same thing. Or Annie's R-Q-W-ignite-/laugh.
The thing is that it is on the opponent to be able to prevent themselves from getting into this ideal situation. Do like Blitzcrank and make sure there's some minions between you and her so she can't Q you. Stand somewhat to the side of the minions so she has to choose to use E to farm or to harass. She can't do both unless you let her. If she walks up to Auto you to proc the passive, make sure you have a way to make her pay (varies by champion). I believe this is why you think people are saying "YOU just suck" it's not really that, but you have to limit her opportunities. And only you can do that.
