Yes, you are allowed to cross a cycle lane when changing lanes if you can do so without endangering or obstructing the road users in the cycle lane.
Keep in mind that both cyclists and moped riders are allowed to overtake you on both the left and right side and that they are harder to detect than cars and other larger vehicles. This means that a cyclist or moped rider may suddenly appear next to you, or just behind you, the moment you are about to change lanes.