David,
LabVIEW
must have a display in order to work. But it does not need to be a "real" display (hardware display adaptor). A perfect display for LabVIEW on embedded Linux systems is Xvnc. This has the added bonus of allowing you to connect to the head of your application over TCP-IP via a VNC client.
The Linux version of RealVNC (available at http://www.realvnc.com) comes with Xvnc which creates a virtual display. You can have your LabVIEW apps displayed in this virtual display (and even connect to the display using a VNC client, if you so wish). BTW, this is how folks create embedded LabVIEW systems running on Linux. You might want to check out LabVIEW Graphical Programming, 3rd Ed. and read the chapters in the back of the book which detail
embedding LabVIEW on Linux.
Install RealVNC by running the install script in the installer archive. You can start the Xvnc server on display 13 (or any unused display) with the command "vncserver :13". Run this once, as root, from a terminal. It will ask you for a login password and will create some files that it needs to start-up. Subsequent runs of this command will start Xvnc without user interaction. After Xvnc is running you can launch your LabVIEW App daemons with the command "myApp -display localhost:13"
You can add these commands to /etc/initab so that they launch at startup. You can also monitor them with a cron job, or another watchdog App, and restart them if they crash. However, if you want more subtle and flexible control of starting, stopping, and monitoring your apps, you might want to "daemonize" them using a tool such as daemontools.
Best of luck,
-Jim