You are going to want to review carefully the information that has been provided to delete an account. If that account is currently signed into a device, you will not be able to remove it and would have to provide proof of purchase to remove the Activation Lock on that account.
You don't need access to the actual email address used for the original Apple Account. When you say you no longer have access, it is not clear if you no longer have access to that email or if you no longer have access to that Apple Account. If you forgot the password to that Apple Account, it can be reset even without access to the email address.
Just want to make sure you do not have that original account signed in on any device before deleting and that you realize that all data stored in iCloud for that account and any previous purchase of media and apps will be lost.