Recently reported structural complexity and superconducting transition in lithium under pressure has increased the interest in light alkalis, otherwise considered as simple metals and well known systems under normal conditions. In this work we present an analysis of the pressure induced Fermi surface deformation in lithium with increasing pressure. According to our calculations, under pressure the Fermi surface becomes highly anisotropic and around 30 GPa develops an extended nesting, which could be the origin of the complex phase transitions observed at this pressure via a phonon instability. On the other hand, the phonon softening induced by the observed distortion and nesting in the Fermi surface could also imply an increasing electron-phonon interaction with pressure, which might also allow a better understanding of the observed superconducting transition in lithium at around the same pressure range.