Can I bake a lightmap for a mesh and use that same lightmap when I make a copy?

I have different pieces of a map that I want to make lightmaps for. Is it possible to bake each of these pieces (think of them being modular and I can build a map out of them) and combine them with their lightmaps?

I've been doing google searching for a while and have not found a way to do this. There are questions involving combining meshes' UV coordinates, as well as questions about using the same lightmap in different scenes.

Thank you