First off, turn off your backup software.
Apple menu -> System Preferences -> Time Machine lets you turn off Time Machine.
If using other backup software, pick the backup software from its menu to the right of the Apple logo menu on the upper left corner of the screen and quit it.
Next you'll want attach a second external hard disk and move contents from the LaCie that are exceeding the 85% full mark of the LaCie. All hard drives reach a point of diminishing returns in productivity when they hit this mark. If they were Time Machine backups, the individual backupdb files that are used least often, and don't need to be accessed via the Time Machine backup software can be moved to another drive. If you had been using cloning software, remove the Log files in Library/Logs, System/Library/Logs, Users/Username/Library/Logs from the LaCie. Any iCloud Backup folder can be copied to yet another external hard drive to free room on the LaCie.