Back-analysis of ground motion characteristics, such as earthquake magnitude and peak ground accelerations, in paleoliquefaction studies are most commonly based on empirical CPT- and/or SPT-based correlations that estimate the liquefaction resistance of soil materials of relevance. Laboratory triaxial cyclic tests have not been explored for this purpose to date. Our study investigates the liquefaction resistance of three different beds (with differing grain-size distributions and pumice content) of a single rhyolitic (high-silica) volcanic-ash layer, referred to as Mamaku tephra, that was deposited ~8000 calendar years ago and preserved in lake sediments in multiple extant lakes in the Hamilton lowlands, North Island, New Zealand. Paleoliquefaction features observed in the silty and sandy beds of the Mamaku tephra indicate seismic activity in the past. With our main aim being to back-analyse potential prehistoric earthquakes that might have caused the paleoliquefaction features in Mamaku tephra (and other lacustrine tephras), the following steps were taken: (1) the liquefaction resistance of the three Mamaku tephra beds with different grain sizes and pumice contents from one site (Lake Areare, northern Hamilton lowlands) was investigated using undrained cyclic triaxial testing; (2) a framework extending the laboratory liquefaction resistance results of the tested Mamaku beds at Lake Areare to other Mamaku tephra deposits in the lake sediments across the lowlands was proposed; and (3) the equivalent peak ground acceleration and earthquake magnitude that would have caused liquefaction of all the lacustrine Mamaku tephra deposits across the lowlands (in 13 lakes) were estimated using available empirical correlation methods. A discussion about the limitations of the proposed framework alongside the qualitative implications on the results is also provided. It was found that the Mamaku tephra deposits are very vulnerable to liquefaction and require very low triggering peak ground acceleration to liquefy, i.e., amax in the range between 0.02 and 0.08 g through the range of magnitudes, M = 5–8.5.