Let me see if I understand your issue. You want the same file to act differently depending on which machine opens it. That, in and of itself is not possible. Lightburn stores the settings with the file and when you open the file, those settings load.
What you can do however is import the file rather than open it. Doing it this way will load the graphics with the layer color that it was saved with, but use default layer settings that you would need to change to suit your needs for the project.