When I'm preparing my make-up water before making wine or beer, should I boil it with the lid on (to minimize evaporation of the water) or with the lid off (to maximize evaporation of volatile contaminants, assuming there are any?)
As always, it depends. Boiling uncovered makes mineral content higher, but lets volatile components to evaporate. Boiling covered - opposite. We don't know what's in your water, so we can't reliably tell which is better.
Ideally, mineral content is low, and your water supply uses ozone instead of chlorine-based substances to prevent bacteria growth - then, you can do both with good result.
Typically, as far as I know, even if chlorine based substances are used, amount is small enough not to be noticeable, and boil will not change anything in that matter. So boil fast, short, and covered to prevent increased mineral content. But it's always a good idea to read water profile from your water supply before deciding. Maybe your water would be ideal for Burton styles, only needs 50% more of everything? If so, of course, boil long and uncovered! And so on.