I have a late 2013 macbook pro and want to connect thunderbolt 3 to the thunderbolt 2 ports. Is this possible with an adapter? The https://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter is not it.

No you need an Apple USB-C to USB-A cable or adapter since you mention the Lacie drive only supports the USB protocol. This is one example from the Apple Store:

mophie USB-A Cable with USB-C Connector (1 m) - Apple

Older style Thunderbolt 1/2 only supports the Thunderbolt protocol so it will not work with a USB3 drive.

You can only do that if the Lacie drive supports the Thunderbolt protocol, but you mentioned the Lacie drive only supports the USB3 protocol which means you must use the USB port on the older laptop. I have not looked up the specifications for the Lacie drive to confirm as I am relying on the information you stated in the original post (I know of Lacie, but am not familiar with their various models).

If you want to use a Thunderbolt port on the 2013 laptop, then you need to purchase an external drive that supports the Thunderbolt protocol. A USB-C connector on a device does not mean it supports the Thunderbolt protocol.

Only the USB-C Thunderbolt ports on the newer Macs support both the Thunderbolt protocol and the USB protocol.

I saw the picture before, but the Lacie photo does not show any protocols on the port. You need to get the technical specifications for the exact model drive you have. Most consumer drives like this will be using the USB protocol. You specifically mentioned the Lacie drive supports USB 3.1 Gen 1 which is the USB protocol not the Thunderbolt protocol.

BellaGolfer wrote:

I want to connect the Lacie Rugged hardrives that only have USB 3.1 Gen 1 Type-C Interface

This requires a USB cable like the one I linked in my earlier post.

BellaGolfer:

Welcome to the confusing world of USB-C …

… where different cables may look alike, but offer vastly different capabilities.