Wonder how much O2 really gets used up over a tank. I mean it's not like it's air tight, if you were somehow put in the tank (sans water) you more likely than not would be able to breathe just fine simply because there would be some air holes. So why does a lid reduce oxygen exchange?
First, remember the physics : diffusion rate depends on the difference of concentrations.
With a lid, it is not air tight, but the air is very still, and there is little circulation.
So O2 concentration will drop, CO2 will rise. Not to deadly levels, but it will change.
And in particular, at the surface, because air is still, it could drop quite a bit locally.
That will affect the rate of air exchange.
It can be tested!
Grab some tank water in a cup, quickly drop your PH meter in, and put the cup just outside the tank.
Wait a couple of hours, stirring it occasionally.
Did PH change a lot? If so, you may have poor air exchange.
(Some change is normal)
(No, I don't have numbers, but I think they out there)
It is easy to see also!
Is your lid totally coated with condensation inside?
If so, it is air tight enough that humidity went way up.
That likely means air is stagnant enough to have O2/CO2 variations.