In this paper, we investigate the stability of pullback random attractors for non-autonomous stochastic p-Laplacian lattice systems characterized by random viscosity and multiplicative white noise. Under suitable conditions, we first establish the existence and uniqueness of these pullback random attractors, followed by demonstrating their backward compactness. We ensure the measurability of this class of attractors by proving that two defined attractor classes are equivalent in relation to two different universes. Finally, we explore the asymptotically autonomous stability of pullback random attractors by assuming that the time-dependent external forcing term converges to a time-independent external force as the time parameter approaches negative infinity.