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You can do Time Machine to backup the Mac to your external hard drive. Go to Apple menu > System Preferences. In System Preferences, choose Time Machine. Turn on Time Machine option, click Select Disk or Select Backup Disk and choose the Lacie drive there.
This will start the backup process. For the initial backup, you should leave the Mac turned on and after that, your Mac will do the backups automatically.
If the hard drive isn't formatted for Mac or if you get any error or unable to select that drive in Time Machine, then you need to erase it for Mac.
Connect the drive to your Mac. Then open Disk Utility from Applications > Utilities folder (or search and open Disk Utility using Spotlight search at top right of screen).
In Disk Utility, select the Lacie brand name in left column (the external drive). Click on Erase tab and select Erase. Make sure "Mac OS Journaled (Extended)" option is selected. This will erase it for Mac (it will delete all contents from external drive if you have any files on it)
Then do the initial steps to backup it using Time Machine. Refer this article --> https://support.apple.com/en-in/HT201250
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