From: How to generate a recovery key - Apple Support
- If you forget your Apple ID password and do not know your recovery key, you can try to regain access using your trusted device protected by a passcode.
- "You can [then] generate a new recovery key from Settings or System Preferences on a trusted device signed in with your Apple ID." See the article for details about how to do this on different types of equipment (Apple equipment only).
- Note: "When you generate a recovery key, you can't use account recovery. Account recovery [a process where Apple recovers your account for you] is a process that would otherwise help you get back into your Apple ID account when you don’t have enough information to reset your password." in other words it appears there is nothing Apple can do to help you in this situation.
-In the end: "Using a recovery key is more secure, but it means that you’re responsible for maintaining access to your trusted devices and your recovery key. If you lose both of these items, you could be locked out of your account permanently."
- Read the article for more details.