The log extract you have posted does not indicate an error with the sending of a notification email, but rather simply a log entry that the notification has been attempted and the detail of the service that is failing. The details you have given signify roughly as follows...
The contact name for use in notifications = nagiosadmin;
The server with the issue = localhost;
The service with the issue = HTTP;
The status of the issue = WARNING;
The notification command response by nagios = notify-service-by-email;
The issue summary/detail (for the email) = HTTP WARNING: HTTP/1.1 403 Forbidden