Hi there, based on your trouble, I suggest you rule out the connection problem by trying different cable or adapter first, which is the easiest way.
Step 1: Insert the LaCie drive into your Mac and launch Disk Utility on your device.
Step 2: Select your drive in Disk Utility and click Mount on the top menu bar.
Step 3: Click First Aid on the top menu bar.
When the process ends, Disk Utility will let you know by poping up a notification.