Need help Maintaining Farming Standards as Lux, taking notes.

So I have about 340k mastery points on , I love everything about her and the possibilities she brings to the table. I consider myself a Lux main and always pick her if I need to secure a win. I do, however, hate her unempowered auto attack strength, and her auto attack speed. The animation itself is incredibly painful to watch and I feel like other control mages like ,, or have a much more fluid animation and stronger AA. My farming with them is typically better. If a wave comes crashing into my tower, I have to burn mana just so that I stand a better chance of the last hitting with her passive, otherwise, it takes 2 AA + 1 turret shot for all the caster minions which are impossible with her slow AA animation. Because of this, I feel like I have to burn mana to keep a wave from crashing into my tower. In lane, I will throw out an E only if I can do damage to minions and hit the enemy laner at the same time for maximum usage. I've even contemplated putting on some AD runes for her just so that she doesn't suck so badly at last hitting. I know that's a really dumb idea because she's AP but I feel like you have to wait until the minion has literally 1 health left before hitting it with a unempowered AA. Because of this, by the time laning is over I'll be at maybe 80-90 CS by 15mins. I know i'm about 5 mins behind of hitting the 100 CS mark.

Being behind in farm is only made worse because I've noticed that whenever a bot tower (ours or theirs) is taken, both bot duos roam mid and I end up losing farm because I'm competing with a ADC who has stronger auto attacks. It forces me to blow mana to farm. At this point in the game I will try to do whatever I can to get back in farm by taking jungle camps or side lanes, but more often than not its at these times that my team wants to fight so I feel obligated to be with them. I'll end most games with only about 150-170 CS, which I know - bad.

I really like Lux and I know this is whats stopping me from taking her skill play to the next level. All suggestions appreciated <3