Lux is disgustingly broken.
2 stuns.
aoe slow, aoe damage, unavoidable damage at that now that she can detonate on site. If you're anywhere within 600 range it's impossible to avoid without flash.
10 shields. She can hit every ally with it twice so yes, 10 shields. And even if she doesn't aim she gets two shields by default for herself.
Long range ult that procs passive.
Passive gives her yet even more burst damage.
High range equivalent to Xerath but without any of the negatives Xerath has that makes him balanced.
She doesn't get movement speed penalties.
Her range, while generally shorter than Xerath is not low enough to justify not having penalties akin to Xerath. Nevermind that xerath is less overloaded than her:
Single stun
Smaller aoe damage and slow, requires center hit to do max slow and damage
Has to charge up for max range on Q, slow movement speed while doing so
Has to stand still during ult. Lux technically does this too but she only needs to aim once and only stands there for what, 1.5 seconds? Xerath needs at least 3 to fire off his shots.