I agree the primary fermentation needs to be covered and cheese cloth works well for small batches. If making wine from juice I use the lid, when making wine from grapes I cover my fermentation vats (500 L) with a clean drop cloth. You certainly want to prevent fruit flies and other foreign objects from getting into the wine.
I always use tight fitting food-grade plastic sheets to cover my pails. I have, until now, avoided using the lid. But either way, you'll be opening it up to stir your must twice a day, so if you have the lid you may as well make use of it.
First stage fermentation in the primary requires oxygen, and you're going to get enough of it when you remove the lid to stir, so don't worry how tight-fitting it is. The ultimate goal is to avoid fruit flies, etc.