A full external hard drive won't let you save new files or it may cause data loss when you continue adding data to a full disk on a Mac.
But, strangely, Mac says the external hard drive is almost full but it isn't. To solve this problem, you can try to unhide files and delete them, update the disk driver, restart the Mac, repair the external hard drive, format Lacie external disk, etc.
After you delete files and empty the Mac Trash, it should free up space on the drive, but unexpectedly, deleting files doesn't free up space on Mac, the reasons behind this could be hidden files on the external hard drive, outdated disk driver, disk corruption, Mac system errors, and so forth.
Here are some proven fixes you can try:
1. Unhide files on Mac. When you find Mac doesn't show the correct storage of the external hard drive after deleting some files, perhaps some files are hidden and invisible. Try to unhide files with the keyboard shortcut Shift + Command + Period(.) or Terminal, and then delete unwanted files.
2. Update the disk driver. An outdated disk driver could also be the culprit when you delete files to free up space but Mac still says it is almost full. You can head to the Apple menu > System Settings, click General on the sidebar, and choose Software Update to update macOS to the latest.
3. Restart your Mac. A quick fix when Mac performs abnormally. It will terminate all running processes and give Mac a fresh start which could eliminate system-related errors.
4. Repair Lacie hard drive with Disk Utility. Perhaps the Lacie external drive is corrupted so that it says the drive is almost full when it isn't and won't save files to it. You can repair corrupted external drives on Mac with Disk Utility's First Aid feature.
5. Reformat the Lacie external drive. For serious disk errors that can't be fixed by Disk Utility, reformatting is what you can try to quickly get rid of logical errors on the drive. If there are any important files on the drive, you should back them up and proceed to format the external hard drive on Mac.
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