Several instances of Thunderbird Lightning have been setup to use Google Calendar however no seems to know which Gmail email account it is tied to. Is there a way I can find out so that the users can assign the appropriate permissions to who can read and edit the calendar?
In the properties of the calendar you can see the email address of the associated account, but I guess you mean the login credentials?
This is in Tools/Options/Security/Passwords/Saved Passwords
Look for the https://calendar.google.com entry and the username should be alongside it.