Hi Mark thanks for continuing this thread. At this time Lucidchart doesn't currently support a functionality for copying or moving a layer on one page to another. Apologies for any inconvenience this causes! I've logged your request for this feature for review by our development team which they'll consider as the prioritize improvements to Lucidchart. If you have additional use case details you'd like to share via the feature request form linked above in Annika's response they can be very helpful for our team in understanding how to improve the experience for you.
In the meantime I recommend Annika's workaround of duplicating a page entirely including its layers or simply selecting copying and pasting all of the content within a single layer of one page into a new layer of another. Please let me know if you have any questions about this!