Cannot mount LaCie external hard drive to MBP

If the drive doesn't appear in Disk Utility when you have toggled "view all devices" (not "view Volumes"), and it doesn't appear in the output from diskutil, then the device isn't connected at all to the computer. Forget mounting a Volume - there is no disk. That leaves three options:

1. Bad cable;
2. Bad enclosure; or
3. The disk itself is dead.

The fact it appears in the USB device tree actually suggests #3 to me, since a d2 Quadra is a fairly complicated enclosure with its own micro-electronics.

Like I said, the d2 Quadra is a fairly advanced enclosure with electronics to manage multiple ports and allow them to all be used with the disk in the device. A power light may only mean the enclosure has power to it's main board.

What I would do is remove the disk from the enclosure and stick it in a drive dock (something like this: https://eshop.macsales.com/shop/external-drives/owc-drive-dock) - but I already have a dock lying around.. If you can power up the disk and read it in a dock, then pull your data off of it - ad your problem was actually something else in the enclosure, so you could get a different one in theory (might not be worth it though).

If the disk is still dead - then for data recovery you are looking at specialist data recovery. It could be expensive - in the $500 - $1000+ USD range (in the higher end especially if clean-room recovery to directly access the platters is required).