Aatrox gets the same treatment like Azir and Kalista right now. He is kept weak intentionally, since the design of his kit itself is inherently broken. He is not balancable with his current kit, since he is the strongest incarnation of a drain tank Riot ever created.
That mechanic is pretty difficult to balance, they were worried about Warwick since his theme of being a drain tank should stay too. They added clear windows of power, since Warwick is just healing himself if he is under 50% health. That way you get a time window to burst and ignite him.
Aatrox on the other hand is able to heal himself permanently, additionally to every life steal he is buying. That is the big problem.
So just like Azir and Kalista, he has to get a rework before they are able to balance him to be viable. Unfortunately it will take some time til these reworks are going to come. We have to be patient.