A lubricant dispenser comprising a storage container filled with lubricant and a pump, which is connected to or can be connected to the storage container and by means of which lubricant can be pumped out of the storage container, wherein the pump has - a pump housing with an inlet opening and an outlet opening, - a piston that is movably guided in the pump housing in a linear manner and - a drive that acts upon the piston, wherein the pump housing of the pump is connected to or can be connected to the storage container, and wherein the piston can be raised and lowered cyclically in a piston receptacle by means of the drive in order to convey the lubricant from the inlet opening to the outlet opening, characterized in that the piston is designed in a stepped manner with an upper piston surface, which delimits an upper displacement chamber, and a lower piston surface, which delimits a lower displacement chamber and is reduced in comparison with the upper piston surface, wherein the upper displacement chamber adjoins the inlet opening via a first valve and the first valve is acted upon or can be acted upon into a closed home position, wherein a through-opening (12a, 12b), which connects the upper displacement chamber to the lower displacement chamber with the interposition of a second valve, is arranged in or on the piston, wherein the lower displacement chamber transitions into the outlet opening via an outlet channel, wherein lowering of the piston on the one hand causes the first valve to open and lubricant to be drawn from the storage container into the upper displacement chamber due to the development of a negative pressure in the upper displacement chamber and on the other hand causes the second valve to close and lubricant to be pressed from the lower displacement chamber into the outlet channel, and wherein raising of the piston on the one hand causes the first valve to close and on the other hand causes the second valve in the piston to open such that lubricant flows from the upper displacement chamber into the lower displacement chamber and lubricant is also pressed from the lower displacement chamber into the outlet channel. wherein the pump has - a pump housing with an inlet opening and an outlet opening, - a piston that is movably guided in the pump housing in a linear manner and - a drive that acts upon the piston, - a pump housing with an inlet opening and an outlet opening, - a piston that is movably guided in the pump housing in a linear manner and - a drive that acts upon the piston, wherein the pump housing of the pump is connected to or can be connected to the storage container, and wherein the piston can be raised and lowered cyclically in a piston receptacle by means of the drive in order to convey the lubricant from the inlet opening to the outlet opening, characterized in that the piston is designed in a stepped manner with an upper piston surface, which delimits an upper displacement chamber, and a lower piston surface, which delimits a lower displacement chamber and is reduced in comparison with the upper piston surface, wherein the upper displacement chamber adjoins the inlet opening via a first valve and the first valve is acted upon or can be acted upon into a closed home position, wherein a through-opening (12a, 12b), which connects the upper displacement chamber to the lower displacement chamber with the interposition of a second valve, is arranged in or on the piston, wherein the lower displacement chamber transitions into the outlet opening via an outlet channel, wherein lowering of the piston on the one hand causes the first valve to open and lubricant to be drawn from the storage container into the upper displacement chamber due to the development of a negative pressure in the upper displacement chamber and on the other hand causes the second valve to close and lubricant to be pressed from the lower displacement chamber into the outlet channel, and wherein raising of the piston on the one hand causes the first valve to close and on the other hand causes the second valve in the piston to open such that lubricant flows from the upper displacement chamber into the lower displacement chamber and lubricant is also pressed from the lower displacement chamber into the outlet channel.