There are plenty of ways to organise saucepan lids so they don't take up a lot of space. If your pots are made from ferrous metal, why not use a magnetic knife rack? That holds the lids securely and keeps them out of the way until you need them.
This idea comes to us from the folks at The Kitchn. You can either use the same rack as you use for your knives (as in the photo above), or designate a pot lid rack in a specific location. This works with just about any ferrous metal pot lid, including the glass ones with metal rims.