I have an Apple ID that I am no longer associated with but cannot remove it from my App Store purchases or my App Store updating. How do I remove that Apple ID that I don’t have the email for anymore?

You could change the primary email address on the account to an address that you have access to : Change your Apple ID - Apple Support

Or if you no longer want to use that account log out of it everywhere (e.g. Settings > iTunes & App Store etc.) and delete all of its downloads - anything downloaded by an account is permanently tied to the account, so only that account can download updates to its apps etc.

Apple ID email address or password - What to do after you change

Delete the app that you know is from the old Apple ID. That should remove it from your purchase history and pending updates.