Airlock activity is not a good indicator of fermentation. Very rarely will I see any activity. Co2 is probably escaping from another spot. You should see a ring of crud around the container and if you took a hydrometer reading you'll see it decrease.
As long as there's actual fermentation there should be a layer of CO2 to limit oxidation risk. The lid is really mostly to keep creepy crawlers from getting in and other things (like wild yeast) from falling in.