The E change was mainly because it caused problems between higher and lower ping players. I agree it does need a slight nerf because it is near impossible to avoid without some form of mobility. But I would say along the line of reduce damage on the edges type of thing. If it sits, this range expands till it cover the full circle. Only effecting instant E damage without hurting wave clear or setting up kills.
Q change is less important. They're probably trying to make maxing Q first better than E so that E is not so strong while Q has more counterplay. I don't think it'll work as using multiple Q's to do what one E would do sounds pointless.
Lux's cooldown are Q(15-11), W(14-10) and E(10 all ranks). Her cooldowns are not in fact short. But I wouldn't call them long. They are in the middle, leaning slightly to long more than short. Not even her ult I would consider short anymore. Rank 3 is only 50s. While it's slightly shorter than average, it's a shadow of it's former glory in regards of a low CD spell. 80s at rank 1 is a bit more shorter than average though.
Overall her CD's only seem short because she builds heavy CDR. She's a long range mage. She needs her spells up more than she needs more damage. It reduces the time frame someone can take advantage of her abilities being on CD.
Her AP ratios are Q(0.7), E(0.6), R(0.75). Again, nothing amazing. Not low. In the middle. Even her ult is in fact on the weaker side unless it is procing her passive.
Overall: Adjust her E and she'll be fine. Everything else you're just making up out of anger.