<p>In this study, we explore the long-time dynamics of second-order non-autonomous multi-valued stochastic lattice systems characterized by varying coefficients, discrete and unbounded distributed delays. Instead of imposing Lipschitz continuity for the nonlinear terms of the resulting system, we adopt a weaker continuity assumption accompanied by growth conditions, which results in the non-uniqueness of solutions to the associated Cauchy problem. With the lack of Lipschitz conditions, we investigate the global existence of solutions for the system, which generates a multi-valued cocycle. Furthermore, the existence of the pullback attractor is considered. With the combined effects of varying coefficients, multiplicative noise and complex delays, the pullback attractor is time-dependent in the time-dependent phase space in which can be substantiated the well-posedness.</p>