  We investigate the validity of the generalized second law of thermodynamics
in a universe governed by Horava-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
modified 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 Horava-Lifshitz gravity.
