We study random dynamical systems composed of Liverani–Saussol–Vaienti maps with varying parameters, without any mixing assumptions on the base space of random dynamics. We establish a quenched central limit theorem and identify conditions under which the associated limit variance varies continuously and differentiably with respect to perturbations of the random dynamics. Our arguments rely on recent results on statistical stability and linear response for random intermittent maps established by Dragičević et al [J. Lond. Math. Soc. 111 (2025), e70150].
