I'm wondering if anyone here would have any ideas on how I can pipe firstname.lastname@example.org to our ticket system on our server with our email being hosted via Google Apps.
Is it possible to pipe a specific email address via DNS?
No there is nothing you can do with DNS. There is probably no way for Google apps mail to directly feed to a pipe.
You could either setup an alias in google apps that forwards to an email address that is hosted on your ticket system server.
You could also setup something like fetchmail to retrieve the email via pop/imap and then send the received messages to ticket system. Here is a page about how to use fetchmail with rt. The exact details would depend on what ticketing system you are using.
What Zoredache said...
Or you could setup a sub-domain (helpdesk.domain.com or whatever) with MX records that point to your helpdesk system and then auto-forward (in the Gmail Settings) email@example.com to firstname.lastname@example.org.
You'll just need to make sure that your helpdesk system can be setup to use a smarthost/relay (which would be Google, authenticating as email@example.com) so that any responses it sends out have firstname.lastname@example.org as the reply-to field.
You might just be able to "spoof" email@example.com as your help desk's outgoing email account, but I don't know if you have any SPF records setup and/or if your Internet connection permits outgoing 25 to send mail directly.