Make sure you have given Lightroom Classic permission to access external disks. This is done in System Preferences->Security and privacy->Privacy tab. Scroll down to Files & Folders and look for Lightroom Classic. If it has everything checked, the problem might be that your external is not formatted correctly or that the folder you are trying to write to on the external has the wrong permissions. If it is an NTFS format disk, you won't be able to write to it. Do a get info on the disk in Finder and look for the format. It should be "Mac OS Extended (Journaled)" or APFS (if it is a SSD). If it is NTFS, it needs to be reformatted or you need to use a third party extension that allows Mac OS X to write to it. This is very common as many external disks come formatted as NTFS as that is what is typical in windows land.
If the disk is formatted correctly, do a get info on the folder you are trying to write into and check that you have write permissions in that folder. If not, fix them.
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