<p>This paper is concerned with the longtime behavior of the non-autonomous stochastic Schrödinger delay lattice systems driven by superlinear noise. We first derive the uniform pullback estimates of the segment process of solutions in probability and then apply the method of uniform tail-ends estimates of solutions to prove the pullback asymptotic compactness of the dynamical system generated by the transition probability operators on the space of probability measures, from which we obtain the existence and uniqueness of pullback measure attractors of the stochastic system. By using the uniform higher-order moment estimates, we further show the upper semicontinuity of these pullback measure attractors as the delay approaches zero. Under additional conditions, we prove the measure attractor is actually an evolution system of probability measures and establish the convergence rate of the system in the Wasserstein metric of order 2 as the delay tends to zero.</p>