We performed numerical experiments on a two-dimensional driven lattice gas, which constitutes a simple stochastic nonequilibrium many-body model. In this model, focusing on the behavior along the direction transverse to the external driving force, we numerically measure transport coefficients and dynamical fluctuations outside the linear response regime far from equilibrium. Using these quantities, we find the validity of the Einstein relation, the Green-Kubo relation and the fluctuation-response relation.