Lost recovery key

With no Trusted Device and no Recovery Key, you will no longer be able to use that Apple ID and will lose all information. This is detailed in the Support Article:

This gives you more control of your account recovery methods and can help prevent an attacker from gaining access to and taking control of your account. However, if you lose your recovery key and can’t access one of your trusted devices, you'll be locked out of your account permanently.

Set up a recovery key for your Apple ID - Apple Support

In order to remove the Apple ID from your device, you will need to erase the iPhone which will bring up the Activation Lock because the device is still locked to that Apple ID. To remove the Activation Lock, you will need to provide the original purchase receipt from Apple or Authorized Apple seller. A third party receipt will not be accepted.

How to remove Activation Lock - Apple Support

The fundamental reason for enabling a recovery key is to block all other methods of resetting a password, so, no.

There’s no path out of both losing the recovery key and forgetting the Apple ID password, because that would be contrary to the whole reason for the recovery key. Which is to block that password reset.

At best, proof of ownership sufficiently convincing to Apple can potentially get the device free of the lost Apple ID.