Ask a chef about what s/he does with his/her pots.... a good one will say "It's not what you do with your pot, it's where you put your lid!"
This is, naturally, a wise model to live by. Here's a pot lid solution from salvaged towel racks.
Step 1: Materials
I found these really cheap (as in quality) wall mount racks ready for incineration/landfill space. These are perfect!
1: Some form of towel rack
2: Mounts for said towel racks
3: Velcro or screws