There are two ways, the manual way, and the automated way.
Whatever way you chose, of course, be sure that the person asking for that password is an admin of the project this list belongs to.
The automated way requires shell access to firstname.lastname@example.org:
change_pw -l LIST-NAME
It automatically sends a new password to the list admins (and displays it on the screen for you). You just need to check that list admins emails (that can be seen at the bottom of the listinfo page - "list run by email@example.com") are not outdated.
LIST-NAME does not carry the domain part (eg: savannah-hackers and not firstname.lastname@example.org).
[mailman@lists list]$ change_pw -l gnu-search-hackers New gnu-search-hackers password: blahblah
The manual way requires only the site-wide Mailman password. Basically you log in the administrative interface of the list you want to reset the password of, go the Passwords section, type a new password in a text editor, copy-paste it the password and confirmation field of the admin password, and send it by mail to the list admin.