Dean,
Thank you so much for your help.
A Tech person at Lutron told me I could use a 1.5k ohm 20w resistor across the primary side of the coil of a relay to fake out their "Grafik Eye" dimmer into thinking the relay primary coil was a load similar to a light.
The relay would then switch a florescent light with an electronic ballast.
He said that florescent lights have a great spike of current draw when they are first turned on and over time that would ruin the dimmer switch.