Molecular-orbital calculations are performed to elucidate electronic structures and optical properties Of lithium Clusters in which several K-shell electrons are simultaneously excited to the valence levels. It is shown that relaxation of valence electrons around localized core holes influences the photoabsorption near-edge spectra significantly. The spectra in the excited state are modified from those in the ground state due to the presence of initial core holes. Potential energy surfaces are calculated for core-ionized Li(9)(z+) clusters, which exhibit bound states for z <= 3. The present cluster calculations would serve as prototypical models of laser-excited hollow atom solids with applications to X-ray optics.