The only problem I really see with your rivers is the western exit on Pohjaton, and maybe the size of the larger island on the eastern exit. You also have some vanishing rivers in the mountains, how are those draining out? Are they dead seas gathering salt? (Possibly negated by the amount of fresh water from glacier melt not having much time to pick up many salts) or are they draining under ground?
However what was said about the lake draining to the west and east is 99.9% unlikely, it isn't 100% impossible. Personally I would get rid of the western drain because the other option is to explain how the lake straddling the edge of two watersheds and the erosion rates allow for flow change to be roughly the same in the east and west.
A bit of eraser action is easiest
(Or you can just make comments in your world about just how odd of a lake it is.)