congrats on your new lock
Is the key C-shaped? I'm not sure if I knwo what you mean by second generation.
Could you maybe make a pic of the key with blackening out most of the biting but not all of it?
If I'm thkining of the right one the key is really old and the profile is probably no longer protected. That means you are in theory able to have it copied.
You will need an abloy dealer though, (google) I can recommend a reputable and turatable Abloy dealer working nation-wide:
https://securitysnobs.com/I'm not affiliated with them in any way, I'm just a happy reutrning customer of them.
Maybe you can find a local lockie who can help, that would probably be easier, but you can contact them and see if they can help. They are nice people.