Was leaving the intersection in the right lane forbidden in the presented situation?

Why?

You may leave this roundabout using the right lane, visible beside the right-hand kerb at the exit. Taking an exit to the left of your original approach does not itself require you to enter the left lane on the exit road. If you change lanes, you must take particular care and give way to vehicles already in the lane you are entering.

art. 22 ust. 1 i 4 Prawa o ruchu drogowym