Let's check if the Mac can even see the device at all.
Hold the ⌥ option key and click on the menu then click System Information. Highlight USB under Hardware and on the right-side do you see the LaCie drive listed in the USB Device Tree?
If you do not see the device. Try moving the drive to a different USB-C port. Check the cable isn't loose. Perhaps you'll need to unplug the device and plug it back in. Most drives have some sort of activity light when they are active. Check if that light is on solid or blinking. See if you can hear or feel and vibration from the disk spinning.
If you do see the device in System Information under the USB Device Tree, then it is being detected but you aren't seeing it mounted in Finder. Open Disk Utility, do you see the disk listed there? It may be attached but not mounted, click the Mount button in Disk Utility to mount it.
You can also check System Settings -> General -> Time Machine and see if the disk is listed. Most of the time I find that Time Machines are hidden and don't show up on the Desktop, meaning macOS is able to mount them behind the scenes and run a backup. Time Machine disks are only writable by macOS. Users will only have read access to a Time Machine drive.