Can I use the LaCie external drive by Seagate as my back up disk for Time Machine?

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Yes. See: Back up your Mac with Time Machine - Apple Support.

Jack

Yes you can. Ideally, the backup drive used for Time Machine backups should be 2 or 3 times as large as your hard drive is.

That would be fine, just ensure it is formatted correctly in Disk Utility. The correct format is APFS.