It sounds to me like either your lid or the bowl(s) are out of round. Measure both, and if you find one dimension longer than the other, use the tried-and-true WKC 'bear hug'. Rest the long dimension side against your chest, then reach across and give steady, gentle pressure to gradually bring that thing back into round.
(I think metal needs to be 'over-flexed' to change it's dimension, so I'm not sure that laying a lid on a flat surface and pushing down will actually correct the problem. However, if you do have a 'true' (perfectly flat) surface, it will tell you if the rim of the lid or bowl 'rocks' and is out of spec.)