I guess you mean the Korean saying :
"어울리는 뚜껑이 필요한 냄비." [Lit. A pot needs its matching lid.]
talking about "finding one's perfect match'.
It is basically the equivalent of the English "There is a lid for every pot." or "Every pot has its cover".
So: "A lid that does not fit" could be understood as "the wrong match/partner".