The lacto-fermentation process is anaerobic, so does better without the presence of oxygen, but it can explode if there's no where for the gasses to escape, which happens when you stir it, lol.
Yeast needs oxygen to ferment, if I'm not mistaken.I would love someone that has actual knowledge (instead of just me guessing) about it to chime in lol.
Initial ferment needs more air- in that case, I kept it cracked. Glass will explode if the lid is tightened. Mine is in a cooler with the lid closed. Pretty sure it's not airtight.