Hi Jason,
This type is setup is common when customers have WebLink and want to allow the public access to documents hosted in the repository without requiring them to log in.
The user, PUBLIC, would then just be a standard Laserfiche repository user that's configured in the Laserfiche Administration Console. As a user with the necessary privileges, you should be able to log into the Administration Console, view the properties for the PUBLIC user and change the password there.
Once that's done, you'd just need to update the password for the user wherever it has been configured, i.e. the WebLink Administrator's Utility.
Regards