If no box was found at home, and you no longer have the strength or time to buy, then use improvised means. It is definitely worth packing the TV in a bubble film to secure the display. Make sure the film is wrapped tightly and secured with tape. Next, wrap the TV in a blanket and put it in some kind of bag, suitcase (if the monitor is small enough) or a tight fabric bag like a shopper. This method is only suitable for emergency transportation, provided that you are not transporting any other things, and the TV itself is no more than 32 inches in diagonal.

Is it even possible to transport a modern TV lying down and without packaging

No, modern TVs cannot be transported without packaging, in which case the screen will be damaged – you will see broken pixels, scratches, and even internal microcircuits may be damaged (if the item accidentally falls). The position inside the car should be vertical – like at home.