The thing is that Lux is trying to be many different things at once, while not excelling at any of them. She's got a good amount of damage, Plenty of utility and crowd control, safety with her range, but she has her issues as well.
Her long early cooldowns, and her insane mana costs prevent her from being able to spam spells effectively. Her passive also runs counter to the whole premise of her kit, which is her long range. Her shield also means that she loses out on even more potential damage, by not having a 4th damaging spell.
On the flip side, looking from the support role, again cooldowns and mana costs prevent her from being an effective support, as well as the lack of any hard crowd control. Not to mention, her ultimate does nothing beyond dealing damage, which runs counter to being a support.
In Solo Queue, Lux is a great champ because she can do a ton of things, and can adapt to whatever happens. In higher level play however, when people are trying to build specific team comps, you're better off picking something that specializes in a specific niche. Want long range poke/siege, Go Xerath. Want utility? Pick Orianna.
Right now, Lux is balanced because she's a jack of all trades, master of none, and right now, Riot's not going to do anything major because she's not being oppressive, as well as people liking her the way she is, but I wouldn't be surprised if she winds up in the rework department in the future.
One thing's for sure though, her mana costs need to be significantly reduced, because 130 mana on her primary damage spell is insane.
