In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic system must be an invariant measure of the deterministic limiting system as noise intensity approaches zero. We then prove the uniform Freidlin-Wentzell large deviations of solution paths over all initial data and the uniform Dembo-Zeitouni large deviations of solution paths over a compact set of initial data. We finally establish the large deviations of invariant measures by combining the idea of tail-ends estimates and the argument of weighted spaces.