  A lattice version of the driven inelastic Maxwell gas is studied in one
dimension with periodic boundary conditions. Each site $i$ of the lattice is
assigned with a scalar `velocity', $v_i$. Nearest neighbors on the lattice
interact, with a rate $\tau_c^{-1}$, according to an inelastic collision rule.
External driving, occurring with a rate $\tau_w^{-1}$, sustains a steady state
in the system. A set of closed coupled equations for the evolution of the
variance and the two-point correlation is found. Steady state values of the
variance, as well as spatial correlation functions, are calculated. It is shown
exactly that the correlation function decays exponentially with distance, and
the correlation length for a large system is determined. Furthermore, the
spatio-temporal correlation $C(x,t)=\langle v_i(0) v_{i+x} (t)\rangle$ can also
be obtained. We find that there is an interior region $-x^* < x < x^*$, where
$C(x,t)$ has a time-dependent form, whereas in the exterior region $|x| > x^*$,
the correlation function remains the same as the initial form. $C(x,t)$
exhibits second order discontinuity at the transition points $x=\pm x^*$ and
these transition points move away from the $x=0$ with a constant speed.
