  In Ho\v{r}ava-Lifshitz cosmology we use the holographic Ricci-like cut-off
for the energy density proposed by L. N. Granda and A. Oliveros and under this
framework we study, through the cosmic evolution at late times, the sign change
in the amount of non-conservation energy ($Q$) present in this cosmology. We
revise the early stage (curvature-dependent) of this cosmology, where a term
reminiscent of stiff matter is the dominant, and in this stage we find a
power-law solution for the cosmic scale factor although $\omega =-1$. Late and
early phantom schemes are obtained without requiring $\omega <-1$.
Nevertheless, these schemes are not feasible according to what is shown in this
paper. We also show that $ \omega =-1$ alone does not imply a de Sitter phase
in the present cosmology. Thermal aspects are revised by considering the energy
interchange between the bulk and the spacetime boundary and we conclude that
there is no thermal equilibrium between them. Finally, a ghost scalar graviton
(extra degree of freedom in HL gravity) is required by the observational data.
