I doubt that moving the project will change the options of the lightbox. But maybe the selected lightbox does not exist on the other computer? In which case the target will be set to default?This is all good and it works fine until I copy the entire site/project folder to my external drive.
Make sure all add-ins and extensions are the dame on both computers.
I'm sure you can get the options from the page HTML. However,. I cannot help to go through all the code of the pages, because for me it may also take a lot of time to figure out what you have done.