Im having a much the same problem.
This is the error I am getting:
Jul 20 21:33:40 centos postfix/smtpd: NOQUEUE: reject: RCPT from unknown[192.168.0.3]: 554 <firstname.lastname@example.org>: Relay access denied; from=<email@example.com> to=<firstname.lastname@example.org> proto=ESMTP helo=<hsjsmith01>
But when I try and send using my working computer (the one I work off to create solutions to things etc) it comes up with the above message, but when I tried going to send a test email to my gmail.com address from work, it works fine.
Can someone shed some light on as to why this should work and the one from my LAN doesnt?
Its kinda weird lol, any helps wonderfully appreciated though as usual!