AFAIK, the STOVL variant doesn't even have a gun or even decent range (yet). That big fan and its transmission is taking up ammo and storage space and the STOVL requirement means the weight has to be kept down. I don't think the Air Force is willing to trade the performance of the standard JSF for the STOVL vairant.
The F-35 will have a GAU-12U 25mm Gatling gun. Te CTOL version will have it internal, the VTOL version will have it external, like the Harrier does.
My favorite projected weapon system for the F-35 is a laser turret mounted within the fan housing. the fan drive shaft from the turbojet is to be used to turn a generator to give the laser it's power. Sucko for air to air, but a killer for air to ground and anti-missile duty...