  We present a fluctuating hydrodynamic description of a non-polar active
lattice gas model with excluded volume interactions that exhibits
motility-induced phase separation under appropriate conditions. For quasi-one
dimension and higher, stability analysis of the noiseless hydrodynamics gives
quantitative bounds on the phase boundary of the motility-induced phase
separation in terms of spinodal and binodal. Inclusion of the multiplicative
noise in the fluctuating hydrodynamics describes the exponentially decaying
two-point correlations in the stationary-state homogeneous phase. Our
hydrodynamic description and theoretical predictions based on it are in
excellent agreement with our Monte-Carlo simulations and pseudo-spectral
iteration of the hydrodynamics equations. Our construction of hydrodynamics for
this model is not suitable in strictly one-dimension with single-file
constraints, and we argue that this breakdown is associated with micro-phase
separation.
