I believe the problem with laying down a refrigerator is you run the risk of having the liquid state of refrigerant from the hi pressure side of the loop entering the low pressure (vapor) side of the loop. If there is liquid refrigerant entering the low pressure side of your compressor, you run the risk of cracking the compressor since it liquid is considered incompressible.
This is my own theory, but I think it is pretty viable. If you need to lay it down, I would let the system sit back upright for about a day. I would then plug the refrigerator in for about 30 seconds to 1 minute at a time and let it rest for a couple minutes. Maybe repeat 5 times or so.
Good Luck.