Right now Lux's lane phase in both mid and support is just max E and out poke your enemy champion, it's not very fun or rewarding, Gragas was a lot like this. Poke with Q then all in when they're low, you added a ramp up time to Gragas's barrel so why not do the same with Lux's E? You could increase the slow amount to compensate and give her decreased CD on her shield or Q to compensate.
Her E is already incredibly difficult to dodge meaning that in most cases the enemy is going to take free harass simply because they can't dodge it, putting a ramp up time on her E would mean she couldn't do this as effectively anymore and she'd actually have to land other skill shots.
I like the idea of her passive but without attack speed it's very difficult to proc it on every spell, if you put a ramp up damage on her E and inceased Q snare duration it would mean she could Q/auto/ult/auto/E/auto