Discovery of higher temperature superconductivity in MgB₂ brought about  a renewed interest in strongly coupled conventional superconductors.  Surprizingly  Li, one of the simplest possible  solids,  turns out to be  ~20 K superconductor when compressed.  We use  density functional electronic structure and linear response theory to investigate the origin of Li superconductivity and lattice dynamics and to link the effects to the Fermi surface topology.