Forgot password and lost recovery key

Indeed.

If you can't sign in with two-step verification using your Apple ID - https://support.apple.com/HT202649 > If you lost your Recovery Key

What you need to do, because I just went through this, is to erase your hard drive and reload the original OS, which in my case was Maverick. After you achieve that, then you can download the latest version of whatever OS is compatible with your computer which for me was Catalina. This entails multiple steps and you also have to be connected to the internet which you obviously can do with a blank hard drive. I contacted the so called Geniuses at Apple and then could not figure this out for me. It took me plodding through multiple online searches until I gathered the information I needed to accomplish the task. I created a new Apple ID and I thought I wrote it down. I did but it was incorrect. I also never generated a recovery key which you can use to create a new Apple ID but of course, I did not do that either. As a result, my only option was to erase the hard drive and start from scratch. I did with absolutely no help from Apple.

Creating a new Apple ID will not allow you to access any purchases you made while using your old ID.

You will lose your apps, music, etc.

Also, when you use iforgot the end result is Apple sending information via an email at your iCloud.com account (WHIch YOU CANT ACCESS IF YOU’VE FORGOTTEN YOUR PASSWORD- this is why you are here in the first place!)

They asked me to use a device that previously was accessed by the Apple ID, but that device is broken.

Any work around to this? They have not asked me for a recovery key. So, I have not been able to use this method.

 See if you can get a Rescue or Notification  email option.