I can send emails as root and when I go into mutt as root it connects to gmail's smtp servers but if I am a normal user (in this case Nagios) it does not connect to gmail's smtp server and will try to send it as nagios@email@example.com instead of the firstname.lastname@example.org account I have set up. Any help is greatly appreciated.
Your description of the problem is highly vague, so I can only estimate that it is something that can be solved by properly setting up ~nagios/.muttrc so that the sender's email address is email@example.com:
my_hdr From: "Name Here" <firstname.lastname@example.org>
Again this holds if I understand what you're asking.