We present the results from a lithium survey of 23 new alpha Persei candidates discovered by ROSAT. The log N(Li) vs. T_eff distribution of these stars is compared with that of previously known members: the distributions for the two samples are in good agreement, although in the 5000-4700 K T_eff range our sample stars are located on the upper envelope of previously known members. We think that this is most likely due to the X-ray selection bias in our sample. This temperature range is indeed where the rotation-Li connection is most clear. The merged ``old'' + ``new'' sample is then compared both with the Pleiades and the IC 2602 and IC 4665 clusters. alpha Per stars shows a spread in lithium, but such a spread starts to be seen at a lower effective temperature than in the Pleiades. A speculative explanation, connecting the dispersion in lithium to a spread in the timescale for disk dissipation, is given.