Density functional calculations of ground and excited states of Li n (nle8) clusters have been performed, within two different approaches. Using a set of Kohn-Sham orbitals to construct wave functions, the calculation of the oscillator strengths of the electric dipole transitions is performed. Our results have been tested at two levels: first the necessary comparison with the experimental data, second the comparison with high level CI (MRD-CI) calculations. This last point is not a trivial challenge, because such anab initio method leads for small clusters to a highly accurate description of the electronic structure and optical absorption spectra. Finally, this is also a new test for the capability of using Kohn-Sham orbitals to construct physically meaningful wave functions. Transition energies, oscillator strengths and finally optical absorption spectra presented here are in general in reasonable agreement with the experimental data and the MRD-CI calculations. That is very promising for bigger systems, with regard to the modest computational effort (CPU time and memory size) of density functional calculations.