I think there isn't one huge glaring problem that Lux suffers from, but a lot of little/medium things that make her a less viable pick.
- Mana
Probably her biggest issue. Most of her spells cost too much when she hits around level 4. She's pretty much forced to get Athene's no matter what, which isn't that big of a deal but again it doesn't really leave her the option of going Morello's/Tear/RoA.
- Other Champs Can Do What She Does But Better
While not saying that there is a champion that can 1-up all her skills, most of her skills can be done by better champions whether in terms of utility or power. Besides Lux's Iconic Ult which got name-nerfed, her skills aren't as strong as other mid-lane mages. I don't know if people would agree with the following assessment but I'll give it a whirl.
Passive: Illumination - I think when she was first released her passive made a lot of sense. She had to risk more by attacking to get the most out of her spells and it actually differentiated good vs great Lux players. But as time passed, mobility creep pretty much makes her passive not worth procing. Assassins (Ahri, Zed, Talon, etc) who have strong mobility pretty much force her not to AA them because they have easy ways to all-in even if they get rooted. I feel like an okay buff would be to let other people proc it for her so it could boost her support/team potential since she works well in a comp that can protect her or hard cc the team.
Q: Light Binding - 2 Sec Root. Not bad on paper. But her Q missile speed is 1200 and has a small hitbox. Lets compare to other straight skill shots with cc attached to it.
: E--ProjectileSpeed=1587(1600) 1-2 Charm (Way better than root)
: E--ProjectileSpeed=1437(1400) 1.6-2 Stun (Faster and better than a root)
: E--ProjectileSpeed=1559(1600) 1.5 Root (Kind of holds up to the same standard, less root time for faster speed. Has a smaller hitbox I believe)
: E--ProjectileSpeed=1970(2000) (Harder to compare since this is a tank support with a root, but still almost twice as fast!)
: Q--ProjectileSpeed=1513(1500) (Another Utility Mage who's kit is just better than Lux utility-wise. Sure it's a slow but it's 80% and you can safely use it with her E)
: Q--ProjectileSpeed=1173(1200) (Same speed here, but up to 3 sec root and bigger hitbox)
Point is most spells with CC are way faster than Lux and are more reliable in the long run.
W: Prismatic Barrier - I actually like this skill a lot, lots of potential here for a great Lux to thrive in team-fights. I think the problem I encounter most is the fact that it isn't as instant and reliable as other shields. Most other shields from other supports/mages are generally instant (but only affect 1-2 people at most, except for a Mantra-ed Karma Shield). This makes it less reliable since a lot of fights can be decided in the blink of an eye.
E: Lucent Singularity - Her Damage Skill with a slow, but kinda crappy slow. Honestly Ori's W beats this in almost every aspect. The missile speed iirc on this is 1300, which again, if you wanted to compare it makes it relatively easier to dodge than other mages. The recent buffs to let her pre-det were nice, but I think it needs a slight buff in missile speed/utility/mana cost.
**R: Finales Fukeln - What is Final Spark? ** I think her Ult has no major issues. Only thing are it's bugs where it gets mis-aimed randomly.
Overall her kit isn't bad, just lackluster. Lacks strong utility to make her a support, and lacks skills that are reliable to make her a decent mage. I think back in 2011/2012 she was more viable, but now there are just too many champs that do a better job than she does. Kind of how Taric used to be an OP support, but now there are just better supports around.
- Lack of Mobility
I'm going to refer to one of her past nerfs that I wish would get reverted.
v3.05 Balance Update
On top of her long range and wide array of defensive utility, Lux was also among the fastest ranged champions in the game. These changes force Lux to be more mindful of her timing and positioning as opponents now have more opportunities to capitalize on her mistakes.
Base Movement Speed reduced to 330 from 340
I know it's only 10 movement speed, but I feel like it was making her lack of mobility even more crappy. She is a Kiting Mage that has been around for 3 years and has been way too easy to catch nowadays. Moreover with items like
and her lack of strong/reliable CC, she's probably in the same class as Zyra who, hey what do you know sucks in the meta now as well.
- What does she need then?
To be honest I'm not entirely sure. She does great in ARAM and Dominion, but ask her to be in SR and she'll be an easy mid lane to gank or a support that just can't do as well as everyone else.
I think her risk/reward in her kit should be tuned, probably on her passive and W or E. Maybe add MS when she procs her passive so she can escape a bit or let her gain some mana to offset her costs? Her pure skill-shot kit I believe should feel more rewarding.
Moreover I believe she needs to be slightly more defined in either her utility or poke potential. She just doesn't fully excel in either, while other viable mages utility or not, can be more defined as one or the other.
Lastly, when Lux gets behind she is pretty much useless. She ends up doing little to no damage. And the utility in her kit just won't cut it to make plays.
I don't know if that was helpful or even 100% on topic, but I hope that was informative!