A Triple-foil differential Plunger for Exotic Nuclei (TPEN) has been developed to measure the lifetimes of excited states in nuclei with small production cross-sections. TPEN utilises one target foil and two degrader foils to make differential lifetime measurements: directly determining the decay function and its derivative at a single plunger distance setting. The direct measurement of the decay function and its derivative removes the requirement to measure -ray intensities at several target-to-degrader distances, thereby reducing the beam-time required relative to a conventional plunger with a single-degrader foil. This paper describes the commissioning of TPEN in the lifetime measurement of the first excited state in 156Dy using this differential lifetime technique. The 46(2) ps measured lifetime was found to be in good agreement with the 45.6(5) ps deduced from a previous high-statistics experiment using a conventional two-foil plunger. A comparison between the differential mode with TPEN, and that using TPEN as a conventional two-foil plunger reveals that it achieves the same statistical accuracy with a ~4 fold reduction in beam-time in the differential mode, for the reaction and experimental setup used in this work. TPEN opens up new opportunities to study exotic nuclei with lower production cross-sections that were previously not accessible.