The Activation Lock is the Apple Account/Password used to set it up, so the easiest method is to find the information on that account and reset the password to it if you forgot it. More information about the Activation Lock is available here:
About Activation Lock on your Apple Watch - Apple Support
If you are still unable to get access to the account used to set it up, then the only other option is to send in the original purchase receipt as proper documentation and make sure it meets the conditions here for Apple to remove the Activation Lock.
https://al-support.apple.com/#/al/agreement
Without the purchase receipt, then I doubt you will be able to get the lock removed. When in doubt, get as much information as you can about your old account and contact Apple directly here for further assistance.
Contact Apple Support - Apple Support