The invitation feature should work with all authentication methods currently supported by Lufi (LDAP, HTTP headers and htpasswd).
But you can use the send_invitation_with_ldap_user_mail invitation setting only with LDAP and HTTP headers authentication (with htpasswd auth, the mail is sent from mail_sender setting value), and you need to make sure that you have a mail attribute for this two auth methods (if you activate send_invitation_with_ldap_user_mail), which you can specify with mail_attr invitation setting.
The "LDAP only" settings in the invitation setting block applies in fact to HTTP headers auth method (the comments are not up to date).
