You don't say where in the world you are but you may find that your country has an abundance of suitably large paint and wallpaper paste pots on general sale. Next time you're passing a construction waste dumpster/skip, have a look to see if there are any 10l plastic bucket style pots of paint, wallpaper adhesive etc in it

No skips/dumpsters locally? Perhaps a local decorating company will have some old ones they would give away
If you're stuck for those, perhaps a plastic builder's bucket, even if the base is narrower than 28cm; cut the bucket all the way around at the point where the diameter is 29+cm, and it should fit on the bin upside down, sitting so it hangs partly down the sides of the bin
I too was minded that 28cm is a common size for a frying pan. To this end either the glass lid of such a pan or the pan itself, with handle removed, may make for an adequate bin lid. New glass lids are available for a paltry sum on popular auction and shopping sites
If you're looking to fit something like this, may I suggest you look at fitting it into the bin upside down? Even a larger (30cm+) lid will fit well if inverted (U shape, rather than n shape) so its center of gravity is below the rim of the bin
Failing all these, a fabric lid may suffice: an old drawstring bag made of synthetic material may be able to sit over and draw up tightly enough