  We study graviton propagations of scalar, vector, and tensor modes in the
deformed Ho\v{r}ava-Lifshitz gravity ($\lambda R$-model) without projectability
condition. The quadratic Lagrangian is invariant under diffeomorphism only for
$\lambda=1$ case, which contradicts to the fact that $\lambda$ is irrelevant to
a consistent Hamiltonian approach to the $\lambda R$ model. In this case, as
far as scalar propagations are concerned, there is no essential difference
between deformed Ho\v{r}ava-Lifshitz gravity ($\lambda R$-model) and general
relativity. This implies that there are two degrees of freedom for a massless
graviton without Ho\v{r}ava scalar, and five degrees of freedom appear for a
massive graviton when introducing Lorentz-violating and Fierz-Pauli mass terms.
Finally, it is shown that for $\lambda=1$, the vDVZ discontinuity is absent in
the massless limit of Lorentz-violating mass terms by considering external
source terms.
