my Apple ID is an old email address I can no longer access. Do I need to change my Apple ID

You dont need to, but I would recommend you do

How to change:

Change your Apple ID - Apple Support

Good luck!

It’s always best to change your AppleID to an actual working email address that you can receive emails at. If you ever need to go through the password reset or account recovery process, messages from those won’t be received if the email is not a valid, working one. That would mean extra time and effort to get back into your account.

Re: "... It’s always best to change your AppleID to an actual working email address that you can receive email ..."

A very sound recommendation by Mr Black.

I'd also add that you might consider using an e-mail address (or alias) where you don't normally receive e-mail.

This way your AppleID is not exposed and in "wide-circulation."

Apple's @iCloud domain works well for this but there are countless other possibilities.

Just my own 2¢.