Never use petroleum-based products on your hand pump. Use only silicone grease. Hill's silicone grease is NLGI 2, which is ideal for keeping your hand pump in good working condition.
This silicone lube geared specifically toward the temperatures your pump will reach during pumping.
Be sure you do not over-lubricate your pump. Follow the maintenance directions in the owner's manual.
PCP Hand Pump NLGI 2 silicone grease
For all Hill PCP hand pumps (can be used in other manufacturers pumps)