Lux is one of the greatest designed champions, ever.
Lux is one champion that should never ever get a VGU.
She is Riot's first great creation, to explain why she's so incredible (You may want to open a page "List of Champions by release date")... Once upon a time, this genre was made up of point and click abilities. The concept of skillshots was always there, the infamous Butcher/Blitzcrank hook for one. But the idea of a character who completely relies on skillshots is not something that was a commonly thought of design at the time.
The first champion to have mostly skillshots was Ezreal. "Time for a true display of skill!" is not just a joke. However we can agree as innovative as Ezreal was, his abilities are very simple. They are projectiles which deal damage multiple ways. Lux however is a champion who takes it to the next level, all 4 of her abilities are skillshots. Her abilities behave in interesting ways, the detonation on the E being particularly impressive, at the time most area of effect abilities simply happened, the skill expression with her E was something completely new. Her Q was a skillshot hard CC (root), which while it may seem ordinary now, there was only one other skill shot hard CC in league at the time (Morgana). Everybody else had stuns which were point-and-click. The trade-off was she could root 2 enemies rather than just one.
And of course, the ultimate "Final Spark", while simple, is unique and there has never been anything else like it since. It is maybe one of the most iconic and spectacular abilities in League. It is one of the most satisfying and feared abilities in the game.
Lux as with most champions at the time, was not meant to be anything other than a "mage" and was supposed to be figured out by the players - She was built to have interesting abilities that could fulfill multiple roles. The AOE gave her solo lane potential, while the hard CC and shield gave her support potential. Her abilities also could allow for multiple build paths, AP, CDR (at the time), or even more auto-attack based builds due to her passive. This aim at versatility has been a success and Lux has been an often picked Mid and Support for 8 years and not fallen off too badly in either that entire time.
Consider Lux has survived the incredible amount of changes in the game over the years, while only receiving tweeks here and there. The only weakness I can perceive is the reliance on her passive to deal her full potential has held her back from professional play. This is the one and only area that may need looking at, and has for a long time. But even if it isn't, she'll remain a force in pubs.
I think it should be commonly understood Lux (alongside Nidalee and Riven) were really the characters who put League on the map and set it apart. The very concepts of skill expression and combo champions start with those.
Thanks for reading!