Having good waveclear would be an unintended strength. Her E not clearing a single wave is probably a totally intended balance lever, since very few midlaners that aren't fed can do it. Hell, even 
Fizz can't oneshot the mage minions unless he builds some AP and maxes his E, and he actually loses his mobility spell! As Lux you have enough range to aa-farm minions and are suceptible to getting your wave pushed (or, assuming your enemy doesn't have pushing as a strength, your enemy would be the one losing all his/her mana).
Lux is balanced or even slightly strong in lower elos, hence her shield was buffed by adding a very telegraphed reload some time ago, and now her ult is getting buffed only in the case you're killing an enemy with it (most new/bad Lux players miss the ult or hit high hp targets and kill with basic spells). There's been a good deal of Riot discussion about her around the mid season mage update last year iirc.
Fizz can't oneshot the mage minions unless he builds some AP and maxes his E, and he actually loses his mobility spell! As Lux you have enough range to aa-farm minions and are suceptible to getting your wave pushed (or, assuming your enemy doesn't have pushing as a strength, your enemy would be the one losing all his/her mana). Lux is balanced or even slightly strong in lower elos, hence her shield was buffed by adding a very telegraphed reload some time ago, and now her ult is getting buffed only in the case you're killing an enemy with it (most new/bad Lux players miss the ult or hit high hp targets and kill with basic spells). There's been a good deal of Riot discussion about her around the mid season mage update last year iirc.
Ahri, Anivia (after 6), Annie, Sol, Azir, Cass, LB, Morgana, Orianna, Syndra, TF, Veigar, Vel, Viktor, Xerath, Ziggs. These are just ranged mages who can wave clear quite easily. Of course, some like Annie are different because it's short range and she Q's everything, but they all have a spell or two that that can clear it with a short cooldown (looking at Syndra in particular), or those like Cass who has tons of damage over time, she can use her spells and them be back up almost instantly. Lux struggles pretty hard in this area is all I'm saying. Even if they use a spell for minions, they still have other spells if they need to trade or be defensive/offensive with. With Fizz- you can't compare because he is a melee assassin.
Even if that weren't the case, her ultimate has a short enough cooldown. They even said she struggles in higher elos in many situations- and some reasons are because of these more dominant mid laners who can waveclear and push, bully, etc. Her shield used to be too strong, of course, but the problem lies with the balance between a shield for herself, and a shield for allies. Buff the shield, the shield becomes too strong. Gut it, and Lux can't use it for herself at all. Level 1 shields for 50 shield strength- about as much as an auto attack. Wanna level it up to rank 2 before maxing Q? It goes up 15 shield strength at the cost of some damage from her Q. It's not ideal but neither is 50 shield strength. I only level it once to save myself/an ally from some damage or an ignite or something like that until I'm forced to max it. I wouldn't call Lux underbalanced at all,and you are definitely right by saying she can be a bit better for lower elos of course, but she definitely has a lot of weaknesses. The biggest one being that she basically relies on her Q in order to combo (lower elos might not dodge but higher elos). Her Q can be readily dodged/taken away by cleanse and maaany other items I mentioned. I'd like to think of it as the same as Amumu- he kinda needs his Q in order to ult (besides flash)- this is a little worse because at least he can tank. Of course I know Riot intended this so it creates balance, but it's now almost readily too easy to get out of her spells.
Again, not complaining about the buff, although I am letting out a little bit of steam so bear with me lol. I'm happy with it, I still just don't think this is going to be that fix she needs for the higher elos. But who knows, maybe it'll surprise me.
Even if that weren't the case, her ultimate has a short enough cooldown. They even said she struggles in higher elos in many situations- and some reasons are because of these more dominant mid laners who can waveclear and push, bully, etc. Her shield used to be too strong, of course, but the problem lies with the balance between a shield for herself, and a shield for allies. Buff the shield, the shield becomes too strong. Gut it, and Lux can't use it for herself at all. Level 1 shields for 50 shield strength- about as much as an auto attack. Wanna level it up to rank 2 before maxing Q? It goes up 15 shield strength at the cost of some damage from her Q. It's not ideal but neither is 50 shield strength. I only level it once to save myself/an ally from some damage or an ignite or something like that until I'm forced to max it. I wouldn't call Lux underbalanced at all,and you are definitely right by saying she can be a bit better for lower elos of course, but she definitely has a lot of weaknesses. The biggest one being that she basically relies on her Q in order to combo (lower elos might not dodge but higher elos). Her Q can be readily dodged/taken away by cleanse and maaany other items I mentioned. I'd like to think of it as the same as Amumu- he kinda needs his Q in order to ult (besides flash)- this is a little worse because at least he can tank. Of course I know Riot intended this so it creates balance, but it's now almost readily too easy to get out of her spells.
Again, not complaining about the buff, although I am letting out a little bit of steam so bear with me lol. I'm happy with it, I still just don't think this is going to be that fix she needs for the higher elos. But who knows, maybe it'll surprise me.
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I'm no Rioter so I can't judge how to balance her, but essentially, yes :p
Or even make her E do a little more base damage, with the hitbox being a little bit smaller. That way, it's AOE still, you can hit all 3 minions and kill them, but you can't hit all 3 minions and the champion so easily. It gives the enemy champion a little lee-way to dodge it, but Lux can also farm a little more effectively.
Also maybe give something to her W as well. I wouldn't say buff it because her shielding 5 enemies with a buffed W would make it 'op' again, but they have to do something with it. Maybe make the early levels stronger or something- not too sure.
On a different note about W, they can even make her shield stronger for allies and such, or maybe make it to where if she hits her W on the way OUT, it's a shield increase. That way it rewards good Lux players for hitting their wand effectively.
Anyways, these are all thoughts of mine and I can't balance a champ, but I hope they keep a lookout for her in the next couple patches!