Haha, more like "Assasin's Creep IV: Black Lag"... the game is clearly poorly optimized as is common for a console port. And common for UbiSchrott.
I have a 2500k running at 4.4GHz and a water cooled Radeon R9 290X running flat out at full speed without thermal throttling. The game will drop below 60fps on highest settings in certain scenes. I get 60fps most scenes but it doesn't feel like 60fps. I think it doesn't take VSync=On well, some games have that problem.
So your "slight lag" with a 7870 seems quite normal, actually it seems to be a very good result.