Can't back up to Time Machine

You have done the basics......things like powering off the LaCie drive, restarting your Mac, and then powering the LaCie back up.......correct?

Right-Click on the LaCie drive on the Mac's desktop and then select Get Info. Look for Format and report on your results.

Open Disk Utility on your Mac Finder > Applications > Utilities > Disk Utility

Select the LaCie drive and run First Aid

Is the LaCie the same format as the primary hard drive? Time Machine doesn't like backing up to APFS from HFS extended GUID, or vice versa.

Disk Utility can tell you the format of every drive when selected. If it has changed, it may be due to a recent upgrade which may require a new format.