In all likelyhood, the camera comes with a driver that exposes ActiveX controls. Once you have this driver, it is pretty simple to make calls to it through LabVIEW. You can look at the ActiveX examples in LabVIEW to see how this is done.
They seem to have a Video capture driver (http://www.axis.com/techsup/software/capture_driver/index.htm) that can stream to third party software. But you would need to find documentation on the dll to know which methods to call.