Some properties of small Li-n clusters (n up to 20) are theoretically investigated, within the density functional theory formalism. The structural properties are examined at the so-called local level of approximation. For very small clusters (n less than or equal to 8), the Li-n conformations which are well known from ab initio calculations are found at very low computational cost. For n>8, optimal starting geometries are generated from two growth patterns, based on the increase of the number of pentagonal subunits in the clusters by adsorption of one or two Li atoms. Several new stable structures are proposed, for which the corresponding vibrational analysis is performed for n up to 18. The study of energetic properties and stability requires the use of gradient-approximated functionals. Such functionals are used for the determination of the relative stability of these clusters. For example, we show that the icosahedral structure is the most favorable geometry for Li-13, whereas this is not the case for Na-13. Ionization potentials and binding energies are also investigated in regard to the size and the geometry of the clusters. Comparison with experimental results and other theoretical approaches (such as nonspherical jellium model) suggests that some combinations of gradient-corrected functionals are more adapted than others to describe Li-n energetic and structural properties.