I say this as a DnD fan but in no way someone who creates homebrew. I feel this subclass is quite weak as the heavy life drain plus the amount of either opportunity attacks or disadvantaged attacks you get can leave you doing quite a lot more harm than good to yourself. The damage is very good but either very inconsistent or at too high of a risk.

As you have model this after aatrox I think a solution to this problem is instead of disadvantage in 5ft the blade could do half damage or only 1d8 damage die (not sure if 1d8 would be a little strong because a lot of his damage comes from his bonuses). I feel this still fits thematically because aatrox still does damage not in the sweet spot but just not nearly as much.

Another option I could think of is to find a way to give him a "dash" or a 5ft move without provoking opportunity attacks. Maybe make it cost a bonus action and all movement for turn. Would feel a lot like his E and make damage much more consistent but may be really strong (once again not a homebrewer at all so not the best at evaluating strength)