Too many connectors may cause trouble when you work with the drive on your Mac, you're suggested to apply a USB-C to USB-B cable to connect the drive to your Mac. After that, go to Disk Utility, click the View button to tap Shows All Devices, and then see if your LaCie hard drive shows up there. If it does, click the Mount button on the top toolbar to make your drive run manually.
Moreover, since you mentioned that the LaCie external hard drive is old, you'd better replace a new external hard drive for future storage work. Do not forget to back up all files on the old LaCie drive because the drive falling happens at any time and leaves no possibility for data recovery.