I assume you are referring to Lightroom Classic. Are the image files on the laptop? Is Lightroom looking for the image files in the same location (same drive name or drive letter) as on the other computer?
I suspect that the external hard drive has a different name or drive letter when connected to the laptop. Check to ensure that the drive letter or name is the same or in the library module right-click on the topmost folder and choose the option to find missing folders or update the folder location and choose the appropriate folder on the laptop that points to the external hard drive.