Hey there nicolemori,
We understand you're experiencing issues with a lost recovery key, and we'd like to help.
Get started here: How to generate a recovery key
This page may also help: Two-step verification for Apple ID
Specifically, check out the section below:
"What if I lose my Recovery Key?
You can sign in to your Apple ID account page and create a new Recovery Key using your Apple ID password and one of your trusted devices.
- Go to your Apple ID account page.
- Sign in with your password and trusted device.
- In the Security section, click Edit > Replace Lost Key.
Keep your new Recovery Key in a safe place. Your old Recovery Key won't work anymore and you can't use it to reset your password or access your account. If you don't see Recovery Key in the Security section, then you are not using two-step verification. "
Please let us know the outcome after giving the above steps a try.
Cheers!