A lift of mass $M$ is accelerating upwards with an acceleration $a$. If the tension in the supporting cable is $T_1$ during upward acceleration and $T_2$ when it accelerates downwards with the same acceleration $a$, then the ratio $T_1 / T_2$ is:
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Moving upwards increases apparent gravity ($g_{\text{eff}} = g+a$), while moving downwards decreases it ($g_{\text{eff}} = g-a$). The ratio of tensions is simply the ratio of their effective gravities.