A container lid assembly (2) that includes an integral pump (6P) so as to create pressure differential within a container. This pressure differential may be lower than atmospheric pressure so as to be at least a partial vacuum within the container. Alternatively, the pressure differential may be a state of higher than atmospheric pressure within the container. There are several features of the present invention that can be used in synergy, but are of value when implemented separately. These features include a pump configuration (120) that activates the reciprocating linear motion of the piston (10) by the rotational movement of a pump actuating element; a contents-dispensing mechanism (150) for removing contents from the container while maintaining the at least a partial vacuum within the container, a vacuum indicator, and a filter configured to filter the gases entering the pump from the interior of the container.