We investigate the validity of the generalized second law of thermodynamics in a universe governed by Hoˇrava-Lifshitz gravity. Under the equilibrium assumption, that is in the late-time cosmological regime, we calculate separately the entropy time-variation for the matter fluid and, using the mod- ified entropy relation, that of the apparent horizon itself. We find that under detailed balance the generalized second law is generally valid for flat and closed geometry and it is conditionally valid for an open universe, while beyond detailed balance it is only conditionally valid for all curvatures. Furthermore, we also follow the effective approach showing that it can lead to misleading results. The non-complete validity of the generalized second law could either provide a suggestion for its different application, or act as an additional problematic feature of Hoˇrava-Lifshitz gravity.
