A system (200, 300, 360, 370, 400, 500) for supplying lubricant to a component (202) of a gas turbine engine (10) having a fan shaft (26) is provided. The system (200, 300, 360, 370, 400, 500) includes a pump (204) drivably couplable to the fan shaft (26) for pumping lubricant to the component (202). The pump (204) includes an inlet (206) for receiving lubricant from a lubricant source (208), an outlet (210) for outputting lubricant to the component (202) and a swashplate (220) movable between at least a first position (P1) and a second position (P2). The system (200, 300, 360, 370, 400, 500) also includes a swashplate actuator (222, 522) for actuating the swashplate (220) between the first position (P1) and the second position (P2) according to whether the fan shaft (26) is rotating in a forward direction (F) or a reverse direction (R) opposite to the forward direction (F).