You could put some lube in it, but that shouldn't happen with a new airbrush, even without lube. Something is hanging up inside. You might want to contact Paasche support and see what they say. The tiniest drop of light oil on the tip of a toothpick applied to the shaft should be enough. If that doesn't fix it, you could unscrew the square nut at the bottom of the air intake. Don't lose the tiny spring that will fall out. Inside, you will see a slot in the valve core. Use a jeweler's screwdriver to keep the valve core from rotating and unscrew the button on top of the trigger. Now push the valve core out the bottom of the airbrush. If there is any gunk on the valve core, clean it and see if it moves freely in the airbrush. You could put just the slightest film of light oil on the shaft. Now put it all back together. When you re-install the square nut, use a round toothpick and be very careful not to cross thread it. It should thread in very easy. It doesn't have to be all the way tight. You can leave it a little loose to lighten trigger pressure.
If that doesn't fix the problem, something is wrong with the airbrush. That is, unless you have allowed a solvent or other contaminant to get inside the valve and cause the little o-ring to swell.
Some airbrushes where the top of the trigger pin passes through a rubber o-ring are more prone to sticking, but that isn't the case with the Paasche H.
I hope that helps.
Don