Why doesn’t the USB-c cable from my LaCie external storage device fit in my MacBook Pro thunderbolt 3 ports

If the cable from LaCie does not fit, it's not a USB-C connector (or it's been damaged or crushed).

Some of my LaCie drives have a USB Micro B Super Speed port on the drive, and they come with a cable with that plug on one end and a USB A plug on the other. to connect those drives to a newer Mac, I use a USB-C to -A adapter.

Identify the ports on your Mac - Apple Support

That's strange. USB-C is the same to every manufacturer. Something else is fiscally wrong with your connectors and ports.

Can you show us an image of the situation, please?

What is the exact model of your MacBook Pro, perhaps you have Thunderbolt 2 instead of Thunderbolt 3.