The unimolecular dissociation of energy rich lithium cluster ions shows that Li-n(+) zdissociate by sequential atom or dimer loss. The binding energies of Li-n(+) (n=4-42) generated in an evaporative ensemble are determined from unimolecular decay, within a well defined time window, and energy constraint. They present a sawtooth behavior vs cluster size less pronounced that it should be from a simple metal model. Odd-even alternation is superimposed on the sawtooth behavior, with odd sized cluster ions being more stable. Cohesive energies per atom of Li-n(+) are deduced from these dissociation energies up to n=40 and from extended photo-induced measurements up to n=95. Cohesive energies per atom of neutral clusters Li-n are derived by combining these ionic cohesive energies with the literature ionization potentials. The linearity of the neutral cluster cohesive energy vs the cluster surface to volume ratio permits a volume and a surface energy to be deduced. These values are compared to the bulk values.