Lux's kit offers 550 base + 225% AP damage from a full combo.
Let's compare some other "good" champions that have different identities. Specifically, a mobile mage, and an assassin.
has 510 base damage + 275% AP damage from a full combo (all 3 W's and all 3 ults). In comparison Lux is insanely OP. Lux has more utility in her kit, and offers more damage (not to mention her skillshots are easier to land, Q passes through 1 target while charm doesn't, and E is harder to dodge than Ahri's Q). Add in that Ahri will almost never deal damage from all 3 W's (at least 1 if not 2 will hit minions) or all 3 ultimates (1 will almost always be to reposition/dodge something). If the mobility to long range is the tradeoff, I agree from this perspective that Lux has a bit too much damage.
For an AP assassin
has 395 base + 245% AP damage from a full combo, PLUS 20 base + 20% AP damage per second from Tibbers.
At level 6 this should be a lot weaker than Lux since the base damage is considerably lower, however the scaling is much better.
So in summary: Lux definitely has too much damage at level 6, but her late game is probably balanced. Her long ranged advantage should be the equalizer to Ahri's mobility and yet she gets oodles of damage and better utility on top of that. Compared to Annie it's an early game to late game scale which is fair, but again Lux's significant range advantage tips the scales too heavily in her favour.
I'd argue that Lux should have the base damage on her Q lowered by 20-40 at rank 1 and increased by 5-10 per level so she reaches the same spot at max rank, and/or her ultimate should be lowered by 50-100 damage at rank 1 and increased by 25-50 per rank to be the same at max rank. All of her AP scalings are okay.