  Based on the Lewkowycz-Maldacena prescription and the fine structure analysis
of holographic entanglement proposed in arXiv:1803.05552, we explicitly
calculate the holographic entanglement entropy for warped CFT that duals to
AdS$_3$ with a Dirichlet-Neumann type of boundary conditions. We find that
certain type of null geodesics emanating from the entangling surface
$\partial\mathcal{A}$ relate the field theory UV cutoff and the gravity IR
cutoff. Inspired by the construction, we furthermore propose an intrinsic
prescription to calculate the generalized gravitational entropy for general
spacetimes with non-Lorentz invariant duals. Compared with the RT formula,
there are two main differences. Firstly, instead of requiring that the bulk
extremal surface $\mathcal{E}$ should be anchored on $\partial\mathcal{A}$, we
require the consistency between the boundary and bulk causal structures to
determine the corresponding $\mathcal{E}$. Secondly we use the null geodesics
(or hypersurfaces) emanating from $\partial\mathcal{A}$ and normal to
$\mathcal{E}$ to regulate $\mathcal{E}$ in the bulk. We apply this prescription
to flat space in three dimensions and get the entanglement entropies
straightforwardly.
