I just poured 2 C of water into my 3C AGG pot and then started added oil to see how much it would take to get a full cover of oil. First attempt - 4 TB (2 oz.). Second attempt, and poking at the oil to try to make it spread out more - 3 TB (1.5 oz). I couldn't get it any thinner than that.
I brought the water to a boil and then tried to pour it off with either the oil or water coming first. No luck. There was no way to separate the oil from the water as I poured.
So if you are packing oil anyway, and want everything to have oil in it, it might work to skip the lid. However, if you don't always want oil in your water, for hot drinks, for example, you'll need a lid. Otherwise, you'd need about 1.5 oz of oil for every time you boil water. I'm keeping my foil lid.
But it was cool to watch the water covered in oil come to a boil without any steam rising at all until just as it boiled.