I got rid of an old 50" Pioneer earlier this year, it was just over 100kg in weight We knew that laying it down was against all advice, so avoided it. The problem I had was that this TV has VERY good castors, we had to remove those before transport otherwise the thing would fly all over the back of the van. Old RP TVs tended to be very bottom heavy (if you are on about the sort that "reaches the floor", unlike modern day ones that can sit on a unit), the top seems light, weak and has a mirror in it and a very flexible screen. I suppose the main question is, would laying it down cause damage to the mirror? Also, would laying it down deform the back of the unit and cause picture problems?
If you can, keep it upright. If you can't keep it upright, then try to support the top half GENTLY against the "floor", perhaps using pillows or some such item. Just make certain you distribute the pressure evenly so there is no stress created between the bottom and top. I suppose it would be best backside down, so the screen looks up.
Keep it upright. It's dangerous to transport a large sheet of glass horizontally: the whole sheet will flex up and down in the middle every time you go over a bump, and it may well shatter under the strain.