Just take the lids that are too large or the ones that barely fit.

The lids too large are a bit annoying because condensed water will slowly drop onto the cooking plate.

As others have mentioned, yes a lid is important because otherwise you would end up with a sauce rather than a soup

Keep it on until the water boils. Then:
When the consistency of the soup is right, cover the pot.
When it’s too thin, leave it uncovered so the surplus water can boil off.
When it’s too thick, no it isn’t!

The two issues with making soup without a lid: heat loss and evaporation.

The first is important as the soup must simmer, not boil. With a lid, you can easily create a mostly uniform heat, without it will probably be too cold at the top, and, as you have to feed more heat, it will most likely be too hot at the bottom.

The second is not unimportant, as you usually cook a good soup for quite some time (my beef broth takes about a day), so evaporation will be quite relevant to the overall consistency of the soup, too. Adding lost water will also add to the temperature inconsistencies.

Without a lid, you lose more water and heat, so it’ll take longer and cost more energy to get the soup to temperature and maintain that temperature, as well as to heat up the extra water that replaces whatever has evaporated. But it’s perfectly doable.

Some stores sell these one-size-fits-all lids that are basically like an inverted dome. Also sometimes sold as “universal pot lid”. A poorly fitted lid is better than no lid in my opinion. You’ll probably save on the energy costs with just a few uses.

The main consequence is that you’re losing a lot more water without a lid. That can be helpful for sauces etc., but a little less so for soup.

Simply try it, you can also add more water to make up for the lost liquid.

My problem is that my pots don’t have lids.

Do you have a non plastic plate that is larger than the opening of the pot? Then you have a lid! I used to have cookware I purchased from thrift stores and yard sales. Some had lids, some did not. But a plate works. Hell even a cutting board (careful if it is wood, mine are bamboo and dishwasher safe) works.

On cooking shows I’ve seen cooks use a frying pan as a lid in a pinch. If you have one of a decent size that might work as a lid for making soup.

Lot of good takes here, but let me explain a few not covered coming from working in a Michelin starred kitchen:

• Uncovered means you’re retaining moisture. Simple as that
• You should ever simmer anything uncovered unless you mean to remove moisture
• Of you want to keep flavors INSIDE the pot, do that before deglazing. Bloom aromatics and the heavier flavors, including spices.
• If you ever hear a recipe telling you to cover a lot AFTER the boiling period has happened, it’s a bullshit internet recipe of nonsense.