The structure and electronic and optical properties of hydrogenated lithium clusters Li(n)H(m) (n = 1-30, m ≤ n) have been investigated by density functional theory (DFT). The structural optimizations are performed with the Becke 3 Lee-Yang-Parr (B3LYP) exchange-correlation functional with 6-311G++(d, p) basis set. The reliability of the method employed has been established by excellent agreement with computational and experimental data, wherever available. The turn over from two- to three-dimensional geometry in Li(n)H(m) clusters is found to occur at size n = 4 and m = 3. Interestingly, a rock-salt-like face-centered cubic structure is seen in Li(13)H(14). The sequential addition of hydrogen to small-sized Li clusters predicted regions of regular lattice in saturated hydrogenated clusters. This led us to focus on large-sized saturated clusters rather than to increase the number of hydrogen atoms monotonically. The lattice constants of Li(9)H(9), Li(18)H(18), Li(20)H(20), and Li(30)H(30) calculated at their optimized geometry are found to gradually approach the corresponding bulk values of 4.083. The sequential addition of hydrogen stabilizes the cluster, irrespective of the cluster size. A significant increase in stability is seen in the case of completely hydrogenated clusters, i.e., when the number of hydrogen atoms equals Li atoms. The enhanced stability has been interpreted in terms of various electronic and optical properties like adiabatic and vertical ionization potential, HOMO-LUMO gap, and polarizability.