Pot lids are the single most annoying thing to store: round, tall, and unwilling to stack. In a small kitchen they usually end up leaning in a cabinet, sliding onto the floor every time the door opens. You have two good options, and both get them out of the cabinet footprint so the shelf they used to occupy can do real work.
Option one: hang them on the wall
A wall-mounted pot lid and cutting board rack ($27) holds lids in vertical slots, so they stop sliding and start hanging in place. It's no-drill, has a drip tray for wet lids, and frees the cabinet they used to occupy. In a kitchen where every shelf is spoken for, moving lids to the wall is a free win you feel every time you cook.
Option two: stand them in a bin
If wall space is gone, a clear handled bin ($17) lets lids stand on edge instead of stacking flat. The handle pulls the bin out like a drawer, so the lid you want is reachable without unloading the shelf. Clear walls mean you see which lid is which at a glance, instead of lifting five to find the one that fits.
Don't stack them flat
Flat stacking is why lids fall: the round shape has nothing to rest against, so the pile shifts every time you pull one. Vertical — on a wall slot or in a bin — is the only stable orientation, and it's also the only one that lets you grab one with one hand while the pot simmers on the stove.
Add the boards while you're at it
Cutting boards have the same problem and the same fix. The wall rack holds both lids and boards, so one mount clears two counter-cluttering categories at once and leaves you with a counter that finally stays clear through a busy week of cooking.
Pick your approach: shop the wall rack or the handled bin, and see the full set.