Most likely it would follow the "path of least resistance" (and downward elevation) and stay in a single course (again I'm far from an expert).

An easy fix would be to have some mountains in the lower left and have one of the 'branches' start from there.

Ultimately, if you have a story related reason for having the river the way it is, then don't worry about it.

Also, a lake will almost never have 2 outlets, eventually as the water level changes one of the outlets will become dominant and the other(s) will dry up.