Should I close the vessel while soaking nuts?

It doesn't really matter much one way or the other, if you do it on the counter. Oj16 is making the case for preventing an insect getting in - at least where I live, this basically never happens. The other concerns in that answer are for me misplaced - some dust will fall in, but it is the same dust I breathe when I walk around in the kitchen, and if it is present in large enough amount to be a concern, something should be done about the kitchen, not about the beans! And putting a lid on something never made it pathogen-free, the bacteria were there before you put the lid and will start happily multiplying once you give them the moisture.

If you do it in the fridge, a lid can prevent smell contamination. Nuts are neither likely to give off much smell (to contaminate other foods) nor are they very "soaking" of other smells the way milk is. So, you can cover them as a kind of best practice, but if you don't, it's unlikely that you will notice much difference.