Do the same thing as a NI Field Engineer - present a little demo-application (related to your app's specifics if possible) which shows how good is LV comparing with possible alternatives. It's your call to choose the example. My suggestion is to have it simple (few icons and wires), self-explanatory, nice front panel and most important performing something that looks complicated. I remember some NI seminars where the image/data acquisition examples were quite impressive for somebody new to LabVIEW.
If you don't have LV, ask NI for a demo CD. As far as I remember, it includes some nice tutorial movies.
Have Fun and Good Luck!