The lid drawer nobody opens.
Every kitchen has one: a drawer of lids that fit nothing, sorted by nothing, opened by nobody. The problem is not storage.
Open the drawer under the pans and count how many lids do not fit anything in it. In a normal kitchen it is about a third. Nobody throws them out, because each one was, at some point, the right lid.
A lid is not a container
Lids only make sense next to what they seal. Separated from the pan, a lid becomes a disc with a diameter, and a drawer cannot tell one diameter from another — so every search becomes a comparison of circles, done by hand, from the wrist.
Why stacking is the wrong axis
Stacked lids nest into a shingled pile, and the one you want is always in the middle of it. The motion of getting it out rearranges the pile, which is why the drawer is never twice the same shape. It is not messy. It is searching, performed every time, with the hands.
The five-second test
Reach in for the lid you need. If you can identify it by touch in five seconds, the system works. If you have to lift it to see it, the system is the thing you are fighting.
What actually fixes it
Standing, not stacking. A lid that is on edge shows its diameter — the only property that matters — from above, in one glance. Any insert that makes lids vertical is doing the real work. The divided tray is secondary.