This is, naturally, a wise model to live by. Here's a pot lid solution from salvaged towel racks.
Step 1: Materials
1: Some form of towel rack
2: Mounts for said towel racks
3: Velcro or screws
Step 2: Hack to Size
Step 3: Attach
Here's something I learned awhile back in my engineering courses.....
When you apply a shear load, the stress will try to peel away from the top surface downward. This is why hooks and such have their screw mounts ABOVE the load rather than below or at the load point. So don't be tempted to apply a small amount of Velcro - apply a bit above the load point.
OR, screw into your cabinets - I would have if I could :)