The E-Mail address from My Account can be changed by navigating to the My Account page, entering the current password and the new E-Mail address. Vaultwarden is supposed to send an E-Mail with a code in order to set the new E-Mail but for closed LAN usage, the E-Mail will more than likely not be sent (and if it is, then it is also likely that E-mail providers will drop the E-Mail as spam given the lack of a FCrDNS E-Mail server).
In order to change the E-Mail anyway, locate the Vaultwarden SQLite database and query the email_new_token column of the users table after using the interface to request a change of E-Mail address (the SQL query being, SELECT email_new_token FROM users). The email_new_token will contain the code necessary to be entered in the Vaultwarden interface in order to be able to change the E-Mail address.