Q: Apple ID has Two Factor Authentication on it. I've forgot my password and lost my trusted device. How can I recover my Apple ID?

Follow the instructions here >  Regain access to your Apple ID with two-factor authentication account recovery - Apple Support

These are your only options.

If you forgot your Apple ID password - Apple Support

https://support.apple.com/en-us/HT201487

Do you mean 2-Step Verification (Two-Factor does not have a Recovery Key)? If so, then unfortunately, if you don't have two of the three required items to sign in, you will not be able to access your Apple ID:

If you lost two or more of the required sign-in items

As noted above, two-step verification requires at least two of the items below to sign in successfully:

• Your Apple ID password
• Access to one of your trusted devices
• Your Recovery Key

If you've permanently lost any two of these items, you can't sign in or regain access to your account. You'll need to create a new Apple ID. You can create a new one from the Apple ID site.

Here is the article FYI: If you can't sign in with two-step verification using your Apple ID - Apple Support

Sorry

GB