Is it possible to transfer the lighting families used in one project to another?
Yes, different ways.
If it is only a few families you can do the following. Open both projects In the projects containing the lights. Select a family in the project browser. Press edit family (this opens the family in the family editor) and you can click load into project and sselect the new project.
Other way is to select family in project browers, right click, save. Save it to a folder. Repeat for other families.
In the new project click load family. Go to the same folder and select families.
There are still some other ways. Like grouping the items in your project and then copy and past that group to the new projects.
However the best way is to keep a library of families you use in several projects in a folder on your computer/server.
Louis
Please mention Revit version, especially when uploading Revit files.