The effect of neutrino trapping on the longitudinal dielectric function at low densities has been investigated by using different relativistic mean-field models. Parameter sets G2 of Furnstahl-Serot-Tang and Z271 of Horowitz-Piekarewicz, along with the adjusted parameter sets of both models, have been used in this study. The role of the isovector adjustment and the effect of the Coulomb interaction have also been studied. The effect of the isovector adjustment is found to be more significant in the Horowitz-Piekarewicz model, not only in neutrinoless matter but also in matter with neutrino trapping. Although almost independent to the variation of the leptonic fraction, the instability region of matter with neutrino trapping is found to be larger. The presence of more protons and electrons compared to the neutrinoless case is the reason behind this finding. For parameter sets with soft equations of state at low density, the appearance of a large and negative L(q,q0=0) in some parts of the edge of the instability region in matter with neutrino trapping is understood as a consequence of the fact that the Coulomb interaction produced by electron and proton interaction is larger than the repulsive isovector interaction created by the asymmetry between the proton and neutron numbers.