The pressure would tell you little until all of the liquid is gone - if the "L" in LPG is for liquified. The same would be true if 100% of the volume were liquid - and only then would you know that you've got a very dangerous situation.
If some LPG is being drawn off then the liquid is being cooled as the heat in the liquid is part of the heat of vaporization. At the place were the liquid (below) and gas (above) meet gets very cold - at times you'll see frost. You might try to use temperature - possibly an array of sensors on the side of the tank.
As Nigel suggests, weight might be a good choice too. You could also use two pressure sensors - one at the very top of the tank and one at the very bottom. The pressure at the top will be relatively constant and is related to temperature - the pressure at the bottom is the pressure at the top plus the result of the liquid level - so the difference can be used to determine the level. In terms of safety, I'd avoid this approach unless you truly understand what you are doing.