To unpack / expand on the other posts a little...
In the normal up right orientation, there's liquid CO2 at the bottom of the tank, it literally boils and turns into a gas; that gas on top is what we need to use.
If you were to lay the cylinder on its side, most likely you will get liquid CO2 into the regulator. Were that liquid to make it through to the "low side" of the reg, your pressure will go from 20PSI to 800PSI in a matter of seconds. Obviously the low end can't handle that and you'll likely blow out the reg's relief valve, blow apart your bubble counter, lines will rupture, etc, etc, etc ugliness!!
If your cylinder only has 10 or 20% left, you might get away with laying it down because the liquid would be below the valve stem. But you are playing Russian roulette and that's not a risk worth taking.
And I do have some experience: here's my 20lb rig sitting on the scale after I ran it dry