Density functional (DF) calculations have been performed for lithium clusters Li-n and their monoxides LinO with up to ten atoms. There are numerous stable structures, and new isomers have been found in each family. The structural patterns of the homonuclear and oxide clusters are quite distinct. The combination of DF calculations with molecular dynamics (MD) sheds light on the observed pseudorotation of Li-3 and Li-5. We compare with available experimental data and discuss the bonding and structural patterns in the clusters and their oxides, which are often described as "hyperlithiated."