Probably not going to see this get much attention, but...
Why does Aatrox still pay health costs on his Q and E? Furthermore, why are they % costs?
Other champions who pay health costs have far more reliable ways to regain that health. It's not possible to stop Vlad from using his Q--he might not use it on YOU, but he'll just as happily drain a minion to pay for his stuff. Mordekaiser pays flat health but also gains a percentage of the damage he does as a shield, and he does a LOT of damage--the Q alone pays for itself many times over. Mundo's entire kit works around regeneration, and to top that off, he gets health refunded on his most spammable ability so long as it lands--which, frankly, is not that hard. Zac can be bullied off his bloblets by the right champions, but he pays less than Aatrox and his kit allows him to build resistances, making it less dangerous for him to be at lower amounts of health.
But Aatrox? He pays % health costs, but his regen mechanic is a flat amount based on his AD. This makes health a TERRIBLE stat to build on him. At the same time, he's essentially a melee-range ADC, and is extremely reliant on auto attacks to get anything done, but he has a much harder time both approaching and sticking to champions than his fellow divers Tryndamere, Yi, Wukong, Vi. Xin, and Yasuo. He does less damage than them, he's squishier than they are, he requires too many stats compared to them, and to top all that off, he can neither approach nor escape as well as they do. The ONE thing he's got going for him is that he has mixed AoE damage from his E and R, and that is clearly not enough.
I don't know how to fix Aatrox without a full rework. But removing his % health costs, or changing them to flat costs, on his Q and E would at least allow him to build health and not be punished for it, which would be a nice start.