Will non-USB 3 Lightning to Camera Adapter work for new iPhone Migration?
Apple's support documents only list the "Lightning to USB 3 Camera Adapter" as compatible with this process. If you want to be guaranteed that it works - use that adapter.

You can test your old adapter without fear of breaking. If the "Lightning to USB Camera Adapter" works for you, it will be capped at USB 2 speeds, as it doesn't support higher speeds.