I want to put a spiral lid on top of a container. When the lid opens, then the spiral mechanism will rotate into the container. Is there a name for this mechanism? If not, would something like this be possible?
It sounds like you're talking about an iris diaphragm. This has many parts that slide against each other, and would best be printed as separate parts, then assembled.
No spiral lids that I know of. I'm not sure how they would work, anyway. There are plenty of designs with hemispherical lids -- so-called "Venus" boxes. Check Yeggi: