Sex chromosome evolution is a complex sub-field of population genetics with unresolved questions about how quickly and adaptively these chromosomes should evolve compared to autosomes. One key limitation to existing knowledge is an intense focus on only a handful of taxa, resulting in uncertainty about whether observed patterns reflect general processes or are idiosyncratic to the more widely-studied clades. In particular, the Z chromosomes of female heterogametic (ZW) systems tend to be quickly but not adaptively evolving in birds, while in butterflies and moths Z chromosomes tend to be evolving adaptively, but not always faster than autosomes. To understand how these two observations fit into broader evolutionary patterns, we explore patterns of Z chromosome evolution outside of these two well-studied clades. We utilize a publicly available high-quality genome, gene expression, population, and outgroup data for the salmon louse Lepeophtheirus salmonis, an important aquacultural pest copepod. We find that the Z chromosome is faster evolving than the autosomes, but that this effect is driven by increased drift rather than adaptive evolution. Due to high rates of female reproductive failure, the Z chromosome exhibits only a slightly lower effective population size than the autosomes which is nonetheless sufficient to decrease efficiency of hemizygous selection acting on the Z. These results highlight the usefulness of organismal life history in calibrating population genetic expectations and demonstrate the value of the ever-expanding wealth of modern publicly available genomic data to help resolve outstanding evolutionary questions.