Our first-principles calculations show that if the hydrogen atoms on one of the faces of a graphane sheet (prehydrogenated graphene) are substituted with Li atoms, the resulting monolayer attains a good hydrogen storage capacity of around 3.8 wt % close to the revised Department of Energy (DOE) target. It is observed that Li atoms are strongly hybridized with the monolayer and donate their electrons to the substrate such that their binding energy to the surface becomes around -3.27 eV, which is far larger than the cohesive energy of Li in its metal bulk structure. It indicates that Li atoms on the monolayer are not aggregated or clusterized at high doping concentration and high temperature. Our calculation shows that the binding energy of H2 molecules with the monolayer surface is around -0.1 eV resulting from the electrostatic interaction of the polarized charge of hydrogen molecules with the induced electric field by positively charged Li atoms. Similarly, we have examined the hydrogen storage capacity of Li-substituted prehydrogenated boron nitride (BN) sheet; it is observed that it also has a very good hydrogen storage capability similar to Li-substituted graphane sheet.