I didn't say Lux had the longest range in the game. I just meant-- Because of how she works as a whole. She is able to cast her E while moving away and gaining distance making it hard to catch her if she's at max range. Xerath has longer range because he becomes immobile or less mobile during all of his spells. Q requires a charge up and while it is easy to land if you're good with movement predicting/timing still causes him to wast 1-2 seconds charging and reduces his movement speed.
Xerath is more sustained damage because his ult has charges in which have a travel time and small aoe. Lux can insta-burst 2 people if she lands a binding since she can throw it out in 2 seconds or less. Xerath has 1-1.5 seconds to kill one target if he lands his stun. Even then, ulting means he is rooted in place. It leaves him open for that time which some champions can abuse. Lux, once popping her load onto you, can walk away in that 1-2 seconds where Xerath has 3-4 seconds to bust his load and leave.
Plus, I'd say people are more comfortable playing Lux because she has a shield, a two person root, an AoE scouting tool that has a slow, and uber damage with ult. + She's a girl and that laugh is ultimate taunt.
Xerath got reworked and while he's actually better, no one is interested in playing a long ranged sustained damage mage when they insta-gib someone much quicker.
Ziggs has more range than Lux, but his damage is unreliable in mid-lane so he's being taken bot to siege and get the turret quicker since he's safer in that role when pushing.
tl;dr Lux can't clear minions in the backlane because her main clear is her E+Passive and both have utility attached to them.
and many other mages are all able to kill the backline minions in less than 2-5 seconds. Even 
can push faster than her.
You could say "she can AA the minions after using her E" but she's usually this champion who hugs the tower since everyone wants to camp the typical mid laner with no mobility, doing that is also risky vs champions like 
and maybe others.
has pretty much the same range and yet he has no problem with keeping the lane pushed, even when camped. Every mage is able to push and kill with a whole combo, why Lux can't have that too? It just doesn't feel fair to me.
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