For primary, most seasoned winemakers use a towel or something to cover the fermenter to keep out dust and fruitflies and things. The wine needs oxygen at that time, and it needs to off-gas c02 (which is poisonous to yeast). Stirring it daily to break up the "cap" and resuspend any solids that may form is important, and it's so much easier to stir when there is no lid.
Once the wine gets to 1.010-1.020, it is generally transferred to secondary and then airlocked at that time.
If you have a ton of fruitflies like I do in the fall, then a lid and airlock is a good idea as they seem to get into things without a tight fitting lid, but a towel with a big rubber band around the rim of the bucket works well and keeps those buggers out. This time of year, I would just cover the primary with a towel.
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