<p>In this paper, we study the asymptotic behavior in the distribution sense of solutions for stochastic discrete Klein-Gordon-Schrödinger equations, which are driven by fractional discrete Laplacian and locally Lipschitz nonlinear noise. The existence and uniqueness of solutions as well as weak pullback random attractor for the mean random dynamical systems are proven. And finally, the existence of invariant measures for the fractional stochastic equations is discussed by showing the tightness of a family of probability distributions of solutions via the idea of uniform tail-estimates on solutions.</p>