  In this work, we assume the FRLW Universe which is filled with dark matter
along with dark energy in the framework of Horava-Lifshitz (HL) gravity. The
dark energy is considered as the Linear (Model I) and CPL (Model II)
parametrizations of the equation of state parameter. For both models, we
express the Hubble parameter $H(z)$ in terms of the model parameters and
redshift $z$. To rigorously constrain the model, we have employed a
comprehensive set of recent observational datasets including cosmic
chronometers (CC), Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations
(BAO), Gamma-ray Burst (GRB), Quasar (Q) and Cosmic Microwave Background
Radiation (CMB). Through the joint analysis of this diverse collection of
datasets, we have achieved tighter constraints on the model's parameters. This,
in turn, allows us to delve into both the physical and geometrical aspects of
the model with greater precision. Furthermore, our analysis has enabled us to
determine the present values of crucial cosmological parameters, including
$H_{0}$, $\Omega_{m0}$, $\Omega_{k0}$ and $\Omega_{\Lambda0}$. It's noteworthy
that our results are consistent with recent findings from Planck 2018,
underscoring the reliability and relevance of our models in the current
cosmological context. We also conduct analysis of cosmographic parameters and
apply statefinder and diagnostic tests to explore the evolution of the
Universe. In addition, the AIC and BIC suggest that the $\Lambda$CDM model is
the preferred model among all our considered models. Our investigation into the
models has unveiled intriguing features of the late universe
