While moving a refrigerator lying on its side is permissible, the process requires some precautions. At the end of the move, the mover should bring the refrigerator upright and wait as long as it has been on its side, up to 24 hours, before supplying power.
GE recommends moving refrigerators in an upright position whenever possible. When moving fridges on a dolly, the manufacturer recommends situating the dolly at the side of the refrigerator and never at the back. Place the unit with the hinges facing up to keep the doors closed. Always check the owner's manual because manufacturers require certain models to remain upright when moving.