No, the Arduino Joystick will work like normal one, no Lua.
Lua would be used only for exporting telemetrics to background app, which would translate it for Arduino (not sure how yet) to move motors.
EDIT: Actually, I did some reading on Arduino. Looks like implementing USB HID both way would be difficult or even impossible. That way one could use two Arduinos, as they are pretty cheap - one for Joystick, second for Forcefeedback only, communicating as serial port via USB