  Recently generalizations of the harmonic lattice model has been introduced as
a discrete approximation of bosonic field theories with Lifshitz symmetry with
a generic dynamical exponent z. In such models in (1+1) and (2+1)-dimensions,
we study logarithmic negativity in the vacuum state and also finite temperature
states. We investigate various features of logarithmic negativity such as the
universal term, its z-dependence and also its temperature dependence in various
configurations. We present both analytical and numerical evidences for linear
z-dependence of logarithmic negativity in almost all range of parameters both
in (1+1) and (2+1)-dimensions. We also investigate the validity of area law
behavior of logarithmic negativity in these generalized models and find that
this behavior is still correct for small enough dynamical exponents.
